## Math in Focus Grade 3 Chapter 19 Practice 5 Answer Key More Perimeter

This handy Math in Focus Grade 3 Workbook Answer Key Chapter 19 Practice 5 More Perimeter detailed solutions for the textbook questions.

## Math in Focus Grade 3 Chapter 19 Practice 5 Answer Key More Perimeter

Measure the sides of each figure with a ruler. Then find the perimeter.

Question 1.

5 inches.

Explanation:
Perimeter  of a triangle is the sum of the lengths of the triangle.
the lengths are measured with ruler and the total is  perimeter (P) = 5 inches

Question 2.

10 inches

Explanation:
Perimeter  of a parallelogram is the sum of the lengths of the parallelogram
the lengths are measured with ruler and the total is  perimeter (P) = 10 inches

Question 3.

10 cm

Explanation:
Perimeter  of a pentagon is the sum of the sides length of the pentagon
the lengths are measured with ruler and the total is  perimeter (P) = 10 cm

Complete. Find the perimeter of each figure. Remember to show the correct unit in your answer.

Question 4.

Perimeter
= _______ + _______ + _______ + _______
= ______________
Explanation:
The perimeter P of a rectangle is given by the formula, P=l + w + l + w ,
where l is the length and w is the width of the rectangle.
Perimeter of a rectangle = l + w + l + w ,
= 6 + 4 + 6 + 4
= 20 cm

Question 5.

Perimeter
= _______ + _______ + _______ + _______
= ______________
Explanation:
Perimeter of area = 4s
= 7 + 7 + 7 + 7
= 28 in.

Question 6.

Perimeter
= _______ + _______ + _______ + _______
= ______________
Explanation:
The perimeter P of a rectangle is given by the formula, P= l + w + l + w ,
where l is the length and w is the width of the rectangle.
Perimeter of area = l + w + l + w ,
= 20 + 3 + 20 + 3
= 46 ft

Question 7.

Perimeter
= _______ + _______ + _______ + _______
= _______________
Explanation:
Perimeter of square = 4s
=8 + 8 + 8 + 8
= 32 in.

Complete. Find the perimeter of each figure. Remember to show the correct unit in your answer.

Question 8.
Perimeter = _______ + _______ + _______
= ______________

Explanation:
Perimeter of triangle = l + b + h
5 + 6 + 7 = 18 cm
Perimeter  of a triangle is the sum of the lengths of the triangle,
the lengths are measured with ruler and the total is  perimeter (P)

Question 9.
Perimeter = _______ + _______ + _______ + _______
= ______________

Explanation:
Perimeter = 3 + 4 + 5 + 6 =18 in
Perimeter  of a parallelogram is the sum of the lengths of the parallelogram,
the lengths are measured with ruler and the total is  perimeter (P)

Question 10.

Perimeter = ____________
Explanation:
Perimeter
= 10 + 9 + 15 + 9 + 7
= 50 ft

Question 11.

Perimeter = _____________
Explanation:
Perimeter:
12 + 9 + 4 + 6 +6 = 37 m

Question 12.
Use your ruler or a measuring tape to find the perimeter of each figure or object.

Explanation:
The measurements may vary from one to one,
depends upon the size and shape of the object.
So, we use the square centimeter and inch to estimate the perimeter of the objects.

Question 13.
Use your meterstick or yardstick to measure the perimeter of each object.

Explanation:
Measurements may vary from one to one,
depending upon the size, shape of the objects.
So, we use the square meter and square feet to estimate the perimeter of the objects in our house.

Solve.

Question 14.
Sean walks along the edge of a rectangular field once to look for his lost keychain. How far does he walk?

Explanation:
Perimeter of a rectangle (P) = 2(Length + Width)
P = 2(10+8)
=2(18)
= 36 m

Question 15.
Alyssa wants to decorate this birthday card by pasting ribbon around it. What is the length of ribbon she needs?

38 cm length of ribbon she needs.
Explanation:
Perimeter of a rectangle (P) = 2(Length + Width)
P = 2(12 + 7)
= 38 cm

Question 16.
Owen has two square cardboard pieces. Each side is 6 inches. He places them side by side to make a rectangle. What is the perimeter of the rectangle?

Explanation:
The perimeter P of a rectangle is given by the formula, P= l + w + l + w ,
where l is the length and w is the width of the rectangle.
Perimeter of area = l + w + l + w ,
= 12 + 6 + 12 + 6 = 48 in.

Solve.

Question 17.
Theo wraps tape around the top of this rectangular box twice. What is the length of sticky tape he uses?

Explanation:
The perimeter P of a rectangle is given by the formula, P= l + w + l + w ,
where l is the length and w is the width of the rectangle.
Perimeter of area = l + w + l + w ,
= 30 + 18 + 30 + 18 = 96 cm.

Question 18.
Each student in a group glued a string around a square with a side of 12 centimeters. There are 5 students in the group. What was the total length of string they used?

Explanation:
one student glued a string around a square with a side of 12 centimeters
lets calculated Perimeter of a square P= 4x s
P = 4 x 12
= 48 cm
5 students glued a string around a square with a side of 12 centimeters
5 x 48 cm = 240 cm the total length of string they used

Question 19.
The length of a rectangular pool is 4 times its width. If the perimeter of the pool is 140 meters, find the length and width of the pool.

length is 56 meters and width is 14 meters
Explanation:
Perimeter of a rectangle P=2(l + w)
let width is x and the length is 4x as per the given information
140 = 2(4x + x)
140 = 2(5x)
140 = 10x
x = 14 meters width
length = 4 x = 4 x 14 = 56 m

Question 20.
Four square tables are arranged next to each other to form one large rectangular table. The perimeter of the large rectangular table is 20 meters. What is the perimeter of each square table?

Explanation:
the perimeter of a rectangle P = 2(l+b)
P = 2(4x+x)
=10 x
20 = 10x
x = 2m
the perimeter of each square table
P = 4 s = 4 x 2 = 8 meters.

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## Math in Focus Grade 5 Chapter 1 Practice 4 Answer Key Comparing Numbers to 10,000,000

Go through the Math in Focus Grade 5 Workbook Answer Key Chapter 1 Practice 4 Comparing Numbers to 10,000,000 to finish your assignments.

## Math in Focus Grade 5 Chapter 1 Practice 4 Answer Key Comparing Numbers to 10,000,000

Complete the place-value chart. Then use it to compare the numbers.

Question 1.
Which is greater, 197,210 or 225,302?
Compare the values of the digits, working from left to right.

___ hundred thousands is greater than ___ is greater than
So, ___ is greater than ____
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

A whole number is larger than another if it has more digits. If the number of digits in each number is the same, then look at the digits from left to right. If the left digit is larger in one number, then this is the largest number. If this digit is the same, compare the next digit along to the right.
Now compare the numbers: 197,210 and 222,302
1 is less than 2 so 197,210 is less than 222,302. Because In hundred thousand place 1 is smaller than 2.
197,210<222,302

Fill each with >or <.

Question 2.
128,758 74,906
A whole number is larger than another if it has more digits. If the number of digits in each number is the same, then look at the digits from left to right. If the left digit is larger in one number, then this is the largest number. If this digit is the same, compare the next digit along to the right.

1. We are comparing the numbers 128,758 and 74,906.
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
4. 1 is greater than o because in the first number the hundred thousand place is 1 and in the second number there is no hundred thousand place so it becomes zero.
5. Therefore, 128,758 is greater than 74,906.
6. The comparison symbol for greater than is >, pointing to the smaller number of 74,906.

Question 3.
523,719 523,689
A whole number is larger than another if it has more digits. If the number of digits in each number is the same, then look at the digits from left to right. If the left digit is larger in one number, then this is the largest number. If this digit is the same, compare the next digit along to the right.

1. We are comparing the numbers 523,719 and 523,689.
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
4. Both numbers are having the same digit in the hundred thousand, ten thousand, thousands column.
5. Now we compare the next digit. It means now we have to compare hundreds place and the digits are 7 and 6.
6. 7 is greater than 6 in order of digits.
7. Therefore, 523,719 is greater than 523,689.
8. The comparison symbol for greater than is >, pointing to the smaller number of 523,689.

Question 4.
89,000 712,758
A whole number is larger than another if it has more digits. If the number of digits in each number is the same, then look at the digits from left to right. If the left digit is larger in one number, then this is the largest number. If this digit is the same, compare the next digit along to the right.

1. We are comparing the numbers 89,000 and 712,758.
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
4. 0 is less than 7 because the first number in the hundred thousand place is 0 because there is no digit in that place and in the second number the digit of hundred thousand place is 7.
5. Therefore, 89,000 is less than 712,758.
6. The comparison symbol for less than is <, pointing to the greater number of 712,758.

Question 5.
635,002 635,100
A whole number is larger than another if it has more digits. If the number of digits in each number is the same, then look at the digits from left to right. If the left digit is larger in one number, then this is the largest number. If this digit is the same, compare the next digit along to the right.

1. We are comparing the numbers 635,002 and 635,100.
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
4. Both numbers are having the same digit in the hundred thousand, ten thousand, thousands column.
5. Now we compare the next digit. It means now we have to compare hundreds place and the digits are 0 and 1.
6. 0 is less than 1 in order of digits.
7. Therefore, 635,002 is less than 635,100.
8. The comparison symbol for less than is <, pointing to the bigger number of 635,100.

Circle the least number and cross out the greatest number.

Question 6.

The least to greatest is a concept in a number system where the given set of numbers is arranged in an ascending order or least value to the greatest value.
In the given numbers we need to find out the least number and greatest number and then we need to circle for the least number and cross mark for the greatest number.
1. Apply the comparison method to get the least number and greatest number.
2. Compare each digit present in the place values.

Order the numbers from least to greatest.

Question 7.

Note: Least to greatest means ascending order.
Ascending order definition: Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. Ascending order is also sometimes named as increasing order.
For example, a set of natural numbers are in ascending order, such as 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8… and so on. The less than symbol (<), is used to denote the increasing order.

The word ‘ascending’ means going up. Hence, in the case of Mathematics, if the numbers are going up, then they are arranged in ascending order.
The other terms used for ascending order are:
1. Lowest value to highest value
2. Bottom value to Top value
These numbers can be written by using the ascending symbol: 315,679< 615,379< 739,615< 795,316.
The symbol represents that the succeeding number is greater than the preceding number in the arrangement.

Question 8.

Ascending order definition: Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. Ascending order is also sometimes named as increasing order.
For example, a set of natural numbers are in ascending order, such as 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8… and so on. The less than symbol (<), is used to denote the increasing order.

The word ‘ascending’ means going up. Hence, in the case of Mathematics, if the numbers are going up, then they are arranged in ascending order.
The other terms used for ascending order are:
1. Lowest value to highest value
2. Bottom value to Top value
These numbers can be written by using the ascending symbol: 97,632< 245,385< 300,596< 805,342.
The symbol represents that the succeeding number is greater than the preceding number in the arrangement.

Question 9.

_______ millions is less than ____________________ millions.
_______ is less than ___________________ .
Answer: 6 million is less than 8 million
6,990,395 is less than 8,079,720.
A whole number is larger than another if it has more digits. If the number of digits in each number is the same, then look at the digits from left to right. If the left digit is larger in one number, then this is the largest number. If this digit is the same, compare the next digit along to the right.
1. We are comparing the numbers 8,079,720 and 6,990,395
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
4. 6 is less than 8 because the digits of the millions place 6 and 8
5. Therefore, 6,990,395 is less than 8,079,720.
6. The comparison symbol for less than is <, pointing to the greater number of 8,079,720.

Question 10.

___ is greater than ____
A whole number is larger than another if it has more digits. If the number of digits in each number is the same, then look at the digits from left to right. If the left digit is larger in one number, then this is the largest number. If this digit is the same, compare the next digit along to the right.
1. We are comparing the numbers 5,096,357 and 1,083,952
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
4. 5 is greater than 1 because the digits of the millions place 5 and 1
5. Therefore, 5,096,357 is less than 1,083,952.
6. The comparison symbol for greater than is >, pointing to the less number of 1,083,952.

Question 11.

___ is greater than ____
A whole number is larger than another if it has more digits. If the number of digits in each number is the same, then look at the digits from left to right. If the left digit is larger in one number, then this is the largest number. If this digit is the same, compare the next digit along to the right.
1. We are comparing the numbers 6,438,671 and 6,412,586
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
3. We start with the place value column on the left. The digits of millions and hundred thousands place are the same.
4. Now compare the next digits.
5. 3 is greater than 1 because the digits of the ten thousands  place 3 and 1
6. Therefore, 6,438,671 is less than 6,412,586.
7. The comparison symbol for greater than is >, pointing to the less number of 6,412,586.

Fill each with > or <.

Question 12.
4,015,280 2,845,000
The greater than symbol in maths is placed between two values in which the first number is greater than the second number. In inequality, greater than symbol is always pointed to the greater value and the symbol consists of two equal length strokes connecting at an acute angle at the right. ( >).

1. We are comparing the numbers 4,015,280 and 2,845,000
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
5. 4 is greater than 2 because the digits of the millions  place 4 and 2
6. Therefore, 4,015,280 is greater than 2,845,000.
7. The comparison symbol for greater than is >, pointing to the less number of 2,845,000.

Question 13.
999,098 1,000,000
A less than symbol is placed between two numbers where the first number is less than the second number. In inequality, less than symbol points to the smaller value where the two equal length strokes connect at an acute angle at the left (<).

1. We are comparing the numbers 999,098 and 1,000,000
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
5. 0 is less than 1 because the digits of the millions  place 0 and 1
6. Therefore, 999,098 is less than 1,000,000.
7. The comparison symbol for less than is <, pointing to the greater number of 1,000,000.

Question 14.
2,007,625 2,107,625
A less than symbol is placed between two numbers where the first number is less than the second number. In inequality, less than symbol points to the smaller value where the two equal length strokes connect at an acute angle at the left (<).

1. We are comparing the numbers 2,007,625 and 2,107,625.
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
5. 0 is less than 1 because the digits of the hundred thousand  place 0 and 1
6. Therefore, 2,007,625 is less than 2,107,625.
7. The comparison symbol for less than is <, pointing to the greater number of 2,107,625.

Question 15.
7,405,319 905,407
The greater than symbol in maths is placed between two values in which the first number is greater than the second number. In inequality, greater than symbol is always pointed to the greater value and the symbol consists of two equal length strokes connecting at an acute angle at the right. ( >).

1. We are comparing the numbers 7,405,319 and 905,407
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
5. 7 is greater than 0 because the digits of the millions place 7 and 0. In the second number, there is no millions place. So it becomes zero.
6. Therefore, 7,405,319 is greater than 905,407.
7. The comparison symbol for greater than is >, pointing to the less number of 905,407.

Order the numbers from greatest to least.

Question 16.

Note: Greatest to least means descending order.
Descending order definition: In simple words, descending order is defined as an arrangement in the highest to lowest format. These concepts are related to decimals, numbers, fractions or amounts of money. This is also known as decreasing the order of numbers.

The symbol used to represent the order in descending form is ‘ > ‘. The given numbers can be represented in this form using the descending symbol as 3,190,000>2,720,000>2,432,000>480,000.

Question 17.

Descending order definition: In simple words, descending order is defined as an arrangement in the highest to lowest format. These concepts are related to decimals, numbers, fractions or amounts of money. This is also known as decreasing the order of numbers.

The symbol used to represent the order in descending form is ‘ > ‘. The given numbers can be represented in this form using the descending symbol as 3,150,000>2,020,000>913,000>513,900.

Find the missing numbers.

Question 18.
738,561 938,561 1,138,561 …

a. 938,561 is ___ more than 738,561.
Explanation:
To get the answer we need to subtract 938,561 and 738,561.

Therefore, 200,000 is more than 738,561.

b. 1,138,561 is ___ more than 938,561.
Explanation:
To get the answer we need to subtract 1,138,561 and 938,561.

Therefore, 200,000 is more than 938,561.
c. ____ more than 1,138,561 is ____
We are looking for a new number which is 200000 more than 1138561.
We will get the new number by adding 200000 to 1138561.
We write it down as:
1138561+200000=1338561

d. The next number in the pattern is ____
In Mathematics, number patterns are the patterns in which a list number follows a certain sequence. Generally, the patterns establish the relationship between two numbers. It is also known as the sequence of series in numbers.

Observation of number patterns can guide to simple processes and make the calculations easier.
By adding 200000 to the number we get the next number.
738,561+200000=938,561
938,561+200000=1,138,561
1,138,561+200000=1,338,561.
Therefore, the next number in the pattern is 1,338,561.

Question 19.
4,655,230 4,555,230 4,455,230 …

a. 4,555,230 is ___ less than 4,655,230.
Explanation:

Therefore, 100000 less to the 4,555,230 from the 4,6555,230.

b. 4,455,230  is ___ less than 4,555,230.

Therefore, 100000 less to the 4,455,230 from the 4,555,230.

c. ___ less than 4,455,230 is ____
Answer: We are looking for a new number which is 4455230 less than 100000.
We will get the new number by subtracting 4455230 from 100000.
We write it down as:
4455230-100000=4355230

d. The next number in the pattern is ____
In Mathematics, number patterns are the patterns in which a list number follows a certain sequence. Generally, the patterns establish the relationship between two numbers. It is also known as the sequence of series in numbers.
Observation of number patterns can guide to simple processes and make the calculations easier.

By subtracting 100000 to the number we get the next number.
4,655,230-100000=4,555,230
4,555,230-100000=4,455,230
4,455,230-100000=4,355,230.
Therefore, the next number in the pattern is 4,355,230.

Find the rule. Then complete the number patterns.

Question 20.

It is an arithmetic pattern.
Definition: The arithmetic pattern is also known as the algebraic pattern. In an arithmetic pattern, the sequences are based on the addition or subtraction of the terms. If two or more terms in the sequence are given, we can use addition or subtraction to find the arithmetic pattern.

The given terms are 230,180    231,180    232, 180    –    –  Now find the missing term in the sequence.
Here, we can use the addition process to figure out the missing terms in the patterns.
In the pattern, the rule used is “Add 1 to the previous term to get the next term”.
Now take the second term 231, 180  If we add 1 to the second term (231), we get the third term (232) and the 180 repeats like that.
Similarly, we can find the unknown terms in the sequence.
First missing term: The previous term is 232. Therefore, 232+1 = 233.
Second missing term: The previous term is 233. So, 233+1 = 234.
Hence, the complete arithmetic pattern is 230, 180  231, 180  232, 180  233, 180  234,180.

Question 21.

It is an arithmetic pattern.
Definition: The arithmetic pattern is also known as the algebraic pattern. In an arithmetic pattern, the sequences are based on the addition or subtraction of the terms. If two or more terms in the sequence are given, we can use addition or subtraction to find the arithmetic pattern.

The given terms are 850, 400   845, 400    840, 400    –    –  Now find the missing term in the sequence.
Here, we can use the subtraction process to figure out the missing terms in the patterns.
In the pattern, the rule used is “subtract 5 to the previous term to get the next term”.
Now take the second term 845, 400  If we subtract 5 to the second term (845), we get the third term (840) and the 400 repeats like that.
Similarly, we can find the unknown terms in the sequence.
First missing term: The previous term is 840. Therefore, 840-5 = 835.
Second missing term: The previous term is 835. So, 835-5 = 830.
Hence, the complete arithmetic pattern is 850, 400  845, 400  840, 400,  835, 400  830, 400.

Question 22.

It is an arithmetic pattern.
Definition: The arithmetic pattern is also known as the algebraic pattern. In an arithmetic pattern, the sequences are based on the addition or subtraction of the terms. If two or more terms in the sequence are given, we can use addition or subtraction to find the arithmetic pattern.

The given terms are 2,650,719  3,650,719  4,650,719    –    –  Now find the missing term in the sequence.
Here, we can use the addition process to figure out the missing terms in the patterns.
In the pattern, the rule used is “Add 1,000,000 to the previous term to get the next term”.
Now take the second term 3,650,719  If we add 1,000,000 to the second term (3,650,719), we get the third term (4,650,719).
Similarly, we can find the unknown terms in the sequence.
First missing term: The previous term is 4,650,719. Therefore, 4,650,719+1,000,000=5,650,719.
Second missing term: The previous term is 5,650,719. So, 5,650,719+1,000,000=6,650,719.
Hence, the complete arithmetic pattern is 2,650,719   3,650,719    4,650,719    5,650,719    6,650,719.

Question 23.

It is an arithmetic pattern.
Definition: The arithmetic pattern is also known as the algebraic pattern. In an arithmetic pattern, the sequences are based on the addition or subtraction of the terms. If two or more terms in the sequence are given, we can use addition or subtraction to find the arithmetic pattern.

The given terms are 6,298,436   5,198,436  4,098,436   –    –  Now find the missing term in the sequence.
Here, we can use the subtraction process to figure out the missing terms in the patterns.
In the pattern, the rule used is “subtract 1,100,000 to the previous term to get the next term”.
Now take the second term 5,198,436  If we subtract 1,100,000 to the second term (5,198,436), we get the third term (4,098,436).
Similarly, we can find the unknown terms in the sequence.
First missing term: The previous term is 4,098,436. Therefore, 4,098,436-1,100,000=2,998,436.
Second missing term: The previous term is 2,998,436. So, 2,998,436-1,100,000=1,898,436.
Hence, the complete arithmetic pattern is 6,298,436  5,198,436  4,098,436  2,998,436  1,898,436.

Complete.

Question 24.
5,083,000 = 5,000,000 + ___ + 3,000
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The value of digit for the given number 5,083,000:
: 5×1,000,000+0x100,000+8×10,000+3×1000+0x100+0x10+0x1
: 5,000,000+0+80,000+3000+0+0+0
: 5,000,000+80,000+3,000.

Question 25.
5,000,000 + 600,000 + 2,000 = ___
Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The value of digit for the given number 5,602,000:
: 5×1,000,000+6×100,000+0x10,000+2×1000+0x100+0x10+0x1
: 5,000,000+600,000+0+2000+0+0+0
: 5,000,000+600,000+2,000.
The number is 5,602,000.

Question 26.
Which is greater, 509,900 or 562,000? ___
Explanation:
A whole number is larger than another if it has more digits. If the number of digits in each number is the same, then look at the digits from left to right. If the left digit is larger in one number, then this is the largest number. If this digit is the same, compare the next digit along to the right.
1. We are comparing the numbers 509,900 and 562,000
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
4. The hundred thousand place digits are the same in both numbers. Now compare the next digits.
5. 6 is greater than 0 because of the digits of the ten thousand place 0 and 6.
6. Therefore, 562,000 is greater than 509,900.
7. The comparison symbol for greater than is >, pointing to the less number of 509,900.

Question 27.
Which is less, 1,020,000 or 1,002,000? ___
1. We are comparing the numbers 1,020,000 and 1,002,000.
2. The order of digits from smallest to largest is 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
4. The millions, hundred thousand place digits are the same in both numbers. Now compare the next digits.
5. 0 is less than 2 because the digits of the ten thousand  place 0 and 2
6. Therefore, 1,002,000 is less than 1,020,000.
7. The comparison symbol for less than is <, pointing to the greater number of 1,020,000.

Question 28.
The value of the digit 1 in 7,1 20,000 is _100,000 and the place value is a hundred thousand.___

What goes around the world but remains in one corner? Write the letters that match the answers below to find out.

Why I choose 80,000:
Explanation:

For the given question the answer: stamp.
1. The stamp is having 5 letters.
2. In the given numbers check for the place values which is having up to 5 places.
3. Now check all the numbers and when coming to the 80,000, the place values are 8 in ten thousand, 0’s is in thousands, hundreds, tens and units place.
4. So, I think 80,000 will be the correct match to those 5 letters.
5. The five letters are ‘s’ ‘t’ ‘a’ ‘m’ ‘p’.

BPCL Pivot Point Calculator

Practice the problems of Math in Focus Grade 1 Workbook Answer Key Chapter 8 Practice 3 Ways to Add to score better marks in the exam.

Example
What is double 1?

Double 1 means to add 1 more to 1.
1 + 1 = 2

Question 1.
What is double 2?

Double 2 means to add ___ more to 2.
___ + ___ = ____
Double 2 means to add 2 more to 2.
2 + 2 = 4

Question 2.
What is double 3?

Double 3 means to add ___ more to 3.
____ + ___ = ___
Double 3 means to add 3 more to 3.
3 + 3 = 6

Question 3.
4 + 4 = ____

Question 4.
5 + 5 = ____

Question 5.
a. 3 + 3 = ____
3 + 4 = ____
3 + 3 = 6
3 + 4 = 7

b. 3 + 3 is double ____
3 + 4 is double ____ plus ____
3 + 3 is double 6
3 + 4 is double 6 plus 1

Complete the number bonds. Then fill in the blanks.

Example

Question 6.

Question 7.

Use doubles facts to complete the addition sentences.

Example

Question 8.

Answer: 0 + 0 = 0

Question 9.

Answer: 6 + 6 = 12

Question 10.

Answer: 5 + 5 = 10

Question 11.

Answer: 8 + 8 = 16

Question 12.

Answer: 9 + 9 = 18

Question 13.

Answer: 10 + 10 = 20

Add the doubles-plus one numbers. Use doubles facts to help you. Then write the doubles fact you used.

Example
5 + 6 = 11
Doubles fact: 5 + 5 = 10

Question 14.
7 + 6 = ____
Doubles fact: ___ + ____ = _____
7 + 6 = 13
Doubles fact: 6 + 6 = 12

Question 15.
7 + 8 = ____
Doubles fact: ___ + ____
7 + 8 = 15
Doubles fact: 7 + 7 = 14

Question 16.
9 + 10 = ____
Doubles fact: ___ + ____
9 + 10 = 19
Doubles fact: 9 + 9 = 18

Question 17.
8 + 9 = ____
Doubles fact: ___ + ____
8 + 9 = 17
Doubles fact: 8 + 8 = 16

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## Math in Focus Grade 5 Chapter 6 Practice 1 Answer Key Finding the Area of a Rectangle with Fractional Side Lengths

Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 6 Practice 1 Finding the Area of a Rectangle with Fractional Side Lengths to score better marks in the exam.

## Math in Focus Grade 5 Chapter 6 Practice 1 Answer Key Finding the Area of a Rectangle with Fractional Side Lengths

Example

Question 1.

A = ____ × width
= ____ × $$\frac{1}{2}$$
= ___ m2
The area of the rectangle is ____ square meters.
Area = length × width
A = 3/5 × 1/2
A = 3/10 m2
Explanation:
In the above image we can observe that length is 3/5 m and width is 1/2 m. The area of the rectangle is 3/10 square meters.

Question 2.

Area = length × width
A = 3/4 × 1/8
A = 3/32 ft2
Explanation:
In the above image we can observe that length is 3/4 feet and width is 1/8 feet. The area of the rectangle is 3/32 square feet.

Find the area of each rectangle.

Question 3.

Area = length × width
A = 4/5 × 5/6
A = 2/3 cm2
Explanation:
In the above image we can observe that length is 4/5 cm and width is 5/6 cm. The area of the rectangle is 2/3 square centimeters.

Question 4.

Area = length × width
A = 3/7 × 2/4
A = 3/14 m2
Explanation:
In the above image we can observe that length is 3/7 m and width is 2/4 m. The area of the rectangle is 3/14 square meters.

Question 5.
A 1 -meter square plot of land is covered by a rectangular patch of grass that measures $$\frac{4}{7}$$ meter by $$\frac{2}{3}$$ meter. What is the area of the patch of grass?

Area = length × width
A = 4/7 × 2/3
A =8/21 m2
Explanation:
In the above image we can observe that length is 4/7 m and width is 2/3 m. The area of the rectangular patch of grass is 8/21 square meters.

Question 6.
Find the area of the top of a rectangle bedside table with a length of $$\frac{3}{4}$$ yard and width that is $$\frac{1}{6}$$ yard less than the length.
Length = 3/4 yard
width = (3/4 – 1/6) yard
= 7/12 yard
Area = length × width
A = 3/4× 7/12
A = 7/16 yard2
Explanation:
The area of the top of a rectangle bedside table with a length of 3/4 yard and width of 7/12 yard is 7/16 square yards.

Find the area of each composite figure.

Question 7.

Area of the rectangle = length ×  width
A = (3/5 ×  1/5) + (3/5 ×  1/5)
A = 3/25 + 3/25
A = 6/25 cm2
Explanation:
To calculate the area we have divided the image into two rectangles.
Length and width of first rectangle are 3/5 cm and 1/5 cm.
So, Area of first rectangle = 3/5 × 1/5 = 3/25 cm2
Length of second rectangle is 3/5 cm (4/5 – 1/5 ) and width is 1/5 cm.
So, Area of second rectangle = 3/5 × 1/5 = 3/25 cm2
Hence, total area of the image = 3/25 + 3/25 = 6/25 cm2
Question 8.

Explanation:
Area of the rectangle = length ×  width
A = (3/9 ×  2/7) + (4/7 ×  1/9)
A = 6/63 + 4/63
A = 10/63 m2
Explanation:
To calculate the area we have divided the image into two rectangles.
Length of first rectangle is 3/9 m (4/9 – 1/9 ) and width is 2/7 m.
So, Area of first rectangle = 3/9 × 2/7 = 6/63 m2
Length and width of second rectangle are 4/7 m and 1/9 m.
So, Area of second rectangle =4/7 × 1/9 = 4/63 m2
Hence, total area of the image = 6/63 + 4/63 = 10/63 m2

Question 9.

Area of the rectangle = length ×  width
A = (4/5 ×  3/5) + (1/10×  1/5)
A = 12/25 + 1/50
A = (24 + 1)/ 50
A = 1/2 m2
Explanation:
To calculate the area we have divided the image into two rectangles.
Length of first rectangle is 4/5 m and width is 3/5 m.
So, Area of first rectangle = 4/5 × 3/5 = 12/25 m2
Length and width of second rectangle are 1/10 m and 1/5 m.
So, Area of second rectangle = 1/10 × 1/5 = 1/50 m2
Hence, total area of the image = 12/25+ 1/50 = (24 + 1)/50 = 1/2 m2

Question 10.

Area of the rectangle = length ×  width
A = (6/7 ×  1/3) + (4/7 ×  2/9) + (2/7 ×  2/9)
A = 2/7 + 8/63 + 4/63
A = (18 + 8 + 4)/63
A = 30/63 Yd2
Explanation:
To calculate the area we have divided the image into three rectangles.
Length and width of first rectangle are 6/7 yard and 1/3 yard.
So, Area of first rectangle =6/7 × 1/3 = 2/7 yd2
Length and width of second rectangle are 4/7 yard and 2/9 yard.
So, Area of second rectangle = 4/7 × 2/9 = 8/63 yd2
Length of third rectangle is 2/7 yard and width is 2/9 yard.
So, Area of third rectangle = 2/7 × 2/9 = 4/63 yd2
Hence, total area of the image = 2/7 + 8/63 + 4/63 = 30/63 yd2

Find the area of the shaded part.

Question 11.

Area of the square = length ×  width
A = (3/5 ×  3/5) – (1/5 × 1/5)
A = 9/25 – 1/25
A = 8/25 in2
Explanation:
To calculate the area we have subtract inner square from outer square.
Length and width of outer square are 3/5 in and 3/5 in.
So, Area of outer square = 3/5 × 3/5 = 9/25 in2
Length and width of inner square are 1/5 in and 1/5 in.
So, Area of inner square = 1/5 × 1/5 = 1/25 in2
Hence, area of the shaded part = 9/25 – 1/25 = 8/25 in2

Question 12.

Area of the rectangle = length ×  width
A = (8/9 × 2/3) – (5/9 × 1/6)
A = 16/27 – 5/54
A = (32 – 5)/54
A = 1/2 m2
Explanation:
To calculate the area we have subtract inner rectangle from outer rectangle.
Length and width of outer rectangle are 8/9 m and 2/3 m.
So, Area of outer rectangle =8/9 × 2/3 = 16/27 m2
Length and width of inner rectangle are 5/9 m and 1/6 m.
So, Area of inner rectangle = 5/9 × 1/6 = 5/54 m2
Hence, area of the shaded part = 16/27 – 5/54 = 27/54 = 1/2m2

Easy Pivot Point Calculator

This handy Math in Focus Grade 5 Workbook Answer Key Cumulative Review Chapters 14 and 15 provides detailed solutions for the textbook questions.

Concepts and Skills

Name each solid. Then write the number of faces and vertices, and the shapes of the faces. (Lesson 14.1)

Question 1.

Explanation:
Given solid triangular prism shape has  number of faces -4,
number of vertices-6 and shapes of faces- 8.

Question 2.

Explanation:
Given solid triangular prism shape has  number of faces – 5,
number of vertices – 5 and shapes of faces – 10.

Name the solid formed from each net. (Lesson 14.1)

Question 3.

Explanation:
Given solid formed with the net is pentagonal prism.

Question 4.

Explanation:
Given solid formed with the net is square based pyramid.

Complete. (Lesson 14.2)

Question 5.
A ___ has two parallel and congruent bases that are joined by a curved surface.
Cylinder,

Explanation:
A cylinder is formed by two parallel congurent circular bases and a curved surface that connects
the bases.

Question 6.
A ____ does not have any edges or vertices, and has the same distance
across any line through its center.
Circle,

Explanation:
A circle does not have any edges or vertices, and has the same distance
across any line through its center.

Question 7.
A _____________ has one vertex, a circular base, and a curved surface.
Cone,

Explanation:
A cone has one vertex, a circular base, and a curved surface.

Question 8.
A sphere has no ___ and________ surfaces.
Faces, Edges, Vertices,

Explanation:
A sphere has no faces, edges, vertices and surfaces.

Find how many unit cubes are used to build each solid. (Lesson 15.1)

Question 9.

_____________ unit cubes
16 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 16 unit cubes,
So, the volume of a 16 unit cubes = 16 X (Side × Side × Side),
= 16 X (1 unit × 1 unit × 1 unit),
= 16 unit cubes.

Question 10.

_____________ unit cubes
13 unit cubes,

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
we have 13 unit cubes,
So, the volume of a 13 unit cubes = 13 X (Side × Side × Side),
=13 X (1 unit × 1 unit × 1 unit),
= 13 unit cubes.

Draw a cube with edges 2 times as long as the edges of this unit cube. (Lesson 15.2)

Question 11.

Explanation:
As a cube has all its sides of the same length.
A unit cube has all its sides of length 1 unit.
Shown the volume of a unit cube = Side × Side × Side,
= 2 units × 1 unit × 1 unit,
= 2 units cubes.

Complete the drawing of this rectangular prism. (Lesson 15.2)

Question 12.

Explanation:
Drawn one rectangular prism on the dot paper,
As given rectangular prism has 4 units X 2 units  X 3 units =
24 unit cubes rectangular prism.

Find the surface area of each prism. (Lesson 15.3)

Question 13.

The surface area of rectangular prism is 1860 cm2,

Explanation:
As the surface area of rectangular prism is
2 X [(width X length) + (height X length) + (height X width)],
= 2 X [(18 cm X 20 cm) + (20 cm X 15 m) + (15 cm X  18 cm)],
= 2 X [(360 cm2) + (300 cm2) + (270 cm2)]
= 2 X [ 930 cm2],
= 1860 cm2.

Question 14.

Surface area of triangular prism = 1,392 cm2,

Explanation:
2 × $$\frac{1}{2}$$ × 12 cm × 16 cm = 192 cm2,
12 cm × 25 cm = 300 cm.2
16 cm × 25 cm = 400 cm.2
20 cm × 25 cm = 500 cm.2
192 cm 2+   300 cm2 + 400 cm2 + 500 cm.2 = 1,392 cm2,
Surface area of triangular prism = 1,392 cm2.

These solids are built using 1-inch cubes. Find and compare their volumes. (Lesson 15.4)

Question 15.

Length = _____4_______ in.
Width = _____4_______ in.
Height = _____4______ in.
Volume = _____64_____ in.3

Length = ______6______ in.
Width = _______4_____ in.
Height = ______3_____ in.
Volume = _____72_____ in.3
Solid _______A____ has less volume than solid ____B______.
Volume of given cube A has  64 cubic units,
Volume of given cube B has  72 cubic units,
Solid A has less volume than solid B,

Explanation:
As we know volume of  solid is l X w X h,
Total surface area of A is 4 in X 4 in X 4 in = 64 cubic units.
Total surface area has 6 in X 4 in X 3 in = 72 cubic units.
Given cube contains 2 less small unit cubes so first we
calculate total surface and subtract missing cubic uints,
therefore, Solid A has less volume than solid B,

Find the volume of each rectangular prism. (Lesson 15.5)

Question 16.

Volume of given rectangular prism is 27 cm3,

Explanation:
Given Length = 3 cm, Width = 1 cm and Height = 9 cm,
Volume of the rectangular prism is lwh = 3 cm X 1 cm X 9 cm = 27 cm3.

Question 17.

Volume of given rectangular prism is 330 m3,

Explanation:
Given Length = 11 m, Width = 6 m and Height =5 m,
Volume of the rectangular prism is lwh = 11 cm X 6 m X 5 m = 330 m3.

Find the volume of water in each container in liters and milliliters. (Lesson 15.5)

Question 18.

Volume of given rectangular prism is 10,290 cm3 which is equal to 10,290 milliliters,

Explanation:
Given Length = 14 cm, Width = 21 cm and Height = 35 cm,
Volume of the rectangular prism is lwh = 14 cm X 21 cm X 35 cm = 10,290 cm3.
as 1 cubic centimeter is equal to 1 milliliters therefore volume of given
rectangular prism is 10,290 cm3 which is equal to 10,290 milliliters.

Question 19.

Volume of given rectangular prism is 1,008 cm3 which is equal to 1,008 milliliters,

Explanation:
Given Length = 7 cm, Width = 9 cm and Height = 16 cm,
Volume of the rectangular prism is lwh = 7 cm X 9 cm X 16 cm = 1,008 cm3.
as 1 cubic centimeter is equal to 1 milliliters therefore volume of given
rectangular prism is 1,008 cm3 which is equal to 1,008 milliliters.

Problem Solving

Question 20.
The length of a rectangular block is 20 inches. Its width is half its length.
Its height is half its width. What is the surface area of the block?
The surface area of a rectangular prism is 1860 cm2,

Explanation:
Given the length of a rectangular block is 20 inches. Its width is half its length.
So width is 10 inches, Its height is half  its width is 5 inches
The surface area of the block is
2 X [(width X length) + (height X length) + (height X width)],
= 2 X [(10 in X 20 in) + (5 in X 20 in) + (5 in X  10 in)],
= 2 X [(200 in2) + (100 in2) + (50 in2)]
= 2 X [ 350 in2],
= 700 in2.

Question 21.
A rectangular piece of poster board measures 70 centimeters by 50 centimeters.
The net of a cube with 12-centimeter edges is cut from it.
What is the area of the poster board left?
The area of the poster board left 2,636 cm2,
Explanation:
Given a rectangular piece of poster board measures 70 centimeters by 50 centimeters,
70 cm X 50 cm = 3,500 cm2, The net of a cube with 12-centimeter edges is cut from it.
Volume of cube is 6 X 12 cm X 12 cm = 864 cm2, therefore the area of the poster board
left is 3,500 cm2 – 864 cm2 = 2,636 cm2.

Question 22.
A rectangular prism is 15 inches long and 12 inches high.
Its width is $$\frac{3}{5}$$ its length. Find its volume.
Volume of a rectangular prism is 1,620 in3,

Explanation:
Given a rectangular prism is 15 inches long and 12 inches high.
Its width is $$\frac{3}{5}$$ its length. So length is
$$\frac{3}{5}$$ X 15 = $$\frac{3 X 15}{5}$$ = 9 inches,
therefore volume is 15 inches X 12 inches X 9 inches = 1,620 in3.

Question 23.
Three cubes with edges measuring 5 inches are stacked on top of one another.
What is the total volume of the 3 cubes?
The total volume of the 3 cubes is 375 in3,

Explanation:
Given three cubes with edges measuring 5 inches are stacked on top of one another.
3 X (5 inches X 5 inches X 5 inches) = 3 X (125 in3) = 375 in3.

Question 24.
The rectangular container shown contains 2 liters of water.
How much more water must be added to fill the container completely?

1,750 cubic cm more water must be added to fill the container completely,

Explanation:
Given rectangular cuboid volume is 10 cm X 25 cm X 15 cm = 3,750 cubic cms as
the rectangular container shown contains 2 liters of water.
Equal to 2 X 1000 = 2,000 cubic cms  so much more water must be
added to fill the container completely is 3,750 cubic cm – 2,000  cubic cm = 1,750 cubic cm.

Question 25.
A container is 28 centimeters long, 1 4 centimeters wide, and 10 centimeters high.
It is half-filled with juice. Kathy pours 500 milliliters of water into the
container to make a juice drink. Find the volume of juice drink in the container now.
Given a container is 28 centimeters long, 1 4 centimeters wide, and 10 centimeters high.
Volume of container is 28 cm X 14 cm X 10 cm = 3,920 cubic centimeters,
It is half-filled with juice. $$\frac{1}{2}$$ X 3,920 = 1,960 cubic centimeters or
1,960 milliliters now Kathy pours 500 milliliters of water into the container
to make a juice drink. Therefore the volume of juice drink in the container now is
1,960 milliliters + 500 milliliters = 2,460 milliliters and 1,000 milliliters = 1 liter,
So 2 L 460 milliliters.

Question 26.
The fish tank shown is filled with 4 liters of water per minute from a faucet.
How long does it take to fill the tank completely?

Long does it will take to fill the tank completely is 6 minutes,

Explanation:
Given the tank has length is 45 cm, width is 16 cm and height is 30 cm,
volume = 45 cm X 16 cm X 30 cm = 2,16,00 cubic cms 21 liters 600 milliliters,
as fish tank shown is filled with 4 liters of water per minute from a faucet,
Long does it will take to fill the tank completely is 21,600 ÷ 4 = 5 minutes 400 ≈ 6 minutes.

Question 27.
A tank with a square base with edges measuring 20 centimeters and a
height of 36 centimeters is $$\frac{2}{3}$$-filled with water.
Each minute, 2 liters of water leak out of the tank through a crack in the bottom.
How long does it take for all the water to leak out?

It will be approximately 5 minutes long for water to leak out,

Explanation:
Given a tank with a square base with edges measuring 20 centimeters
and a height of 36 centimeters, So volume is
20 cm X 20 cm X 36 cm = 14,400 cubic centimeters ,
and tank is filled with $$\frac{2}{3}$$-filled with water means
$$\frac{2}{3}$$ X 14,400 = 9,600 milliliters and each minute 2 liters of
water leak out of the tank through a crack in the bottom is
9,600 ÷ 2,000 = 4.8 5minutes.

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This handy Math in Focus Grade 3 Workbook Answer Key Chapter 16 Practice 3 Addition of Time provides detailed solutions for the textbook questions.

Example

Question 1.

So, 3 h 25 min + 5 h 30 min
= ______ h _______ min.

______ h + ______ h = ______ h
______ min + ______ min = ______ min
______ h + ______ min = ______ h ______ min
3. If the minutes are 60 or more, subtract 60 from the minutes and add 1 to hours
Explanation:
= 3 hours+5 hours
=8 hours.
= 25 min+30 min
= 55 min.
Finally, we get in hours and minutes are 8 hours 55 minutes.

Question 2.

So, 7 h 30 min + 3 h 14 min
= ______ h _______ min.

______ h + ______ h = ______ h
______ min + ______ min = ______ min
______ h + ______ min = ______ h ______ min
3. If the minutes are 60 or more, subtract 60 from the minutes and add 1 to hours
Explanation:
= 7 hours+3 hours
=10 hours.
= 30 min+14 min
= 44 min.
Finally, we get in hours and minutes are 10 hours 44 minutes.

Question 3.

So, 2 h 50 min + 1 h 9 min
= ______ h _______ min.

______ h + ______ h = ______ h
______ min + ______ min = ______ min
______ h + ______ min = ______ h ______ min
3. If the minutes are 60 or more, subtract 60 from the minutes and add 1 to hours
Explanation:
= 2 hours+1 hours
=3 hours.
= 50 min+9 min
= 59 min.
Finally, we get in hours and minutes are 3 hours 59 minutes.

Question 4.
20 min + 55 min = __________ min

Explanation:

The given question is 20 min+55 min=X min.
If we add 20 min and 55 min then we get 20+55=75 min.
To this 75 minutes, we need to convert in hours and minutes.
75 can be written as 60 and 15:
1 hour=60 minute.
And remaining 15 minutes will stay the same.
Finally, 75 min=1 hours 15 minutes.

Question 5.
55 min + 45 min = __________ min

The given question is 55 min+45 min=X min.
If we add 55 min and 45 min then we get 55+45=100 min.
To this 100 minutes, we need to convert in hours and minutes.
100 can be written as 60 and 40:
1 hour=60 minute.
And remaining 40 minutes will stay the same.
Finally, 100 min=1 hours 40 minutes.

Question 6.
4 h 46 min + 2 h 14 min = _____ h _____ min
= ________ h
3. If the minutes are 60 or more, subtract 60 from the minutes and add 1 to hours
Explanation:
= 4 hours+2 hours
=6 hours.
= 46 min+14 min
= 60 min.
Step 3: Apply rule 3. We got 60 minutes. So subtract 60 and add 1 to the hours.
=60-60
=0.
= 6 hours+1
=7 hours.
Therefore,  the answer is 7 hours.

Question 7.
1 h 48 min + 3 h 35 min = _____ h _____ min
= _____ h _____ min
3. If the minutes are 60 or more, subtract 60 from the minutes and add 1 to hours
Explanation:
= 1 hours+3 hour
=4 hours.
= 48 min+35 min
= 83 min.
Step 3: Apply rule 3. We got 60 minutes. So subtract 60 and add 1 to the hours.
=83-60
=23.
= 4 hours+1
=5 hours.
Therefore,  the answer is 5 hours 23 minutes.

Solve.

Question 8.
Grace spends 50 minutes practicing the piano. Then she spends 2 hours 1 5 minutes doing her homework. How long does she spend on the two tasks?
The minutes she spends on the piano=50 min
The time spends on her homework=2 h 15 min
The total time she spends on both works=X
By following some steps we need to calculate the total hours and min.
3. If the minutes are 60 or more, subtract 60 from the minutes and add 1 to hours
Explanation:
= 0+2
=2 hours.
= 50 min+15 min
= 65 min.
Step 3: Apply rule 3. We got 60 minutes. So subtract 60 and add 1 to the hours.
=65-60
=5.
= 2 hours+1
=3 hours.
Therefore,  the answer is 3 hours 5 minutes.

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## Math in Focus Grade 5 Cumulative Review Chapters 1 and 2 Answer Key

Go through the Math in Focus Grade 5 Workbook Answer Key Cumulative Review Chapters 1 and 2 to finish your assignments.

## Math in Focus Grade 5 Cumulative Review Chapters 1 and 2 Answer Key

Concepts and Skills

Write each number in standard form. (Lesson 1.1)

Question 1.
One hundred thousand, seventy _____
100,070,

Explanation:
Standard form or expanded notation is a way of writing numbers to see the math value of individual digits.
Numbers are separated into individual place values to write in numbers.
One hundred thousand = 100 x 1000,
Seventy = 7 x 10,
Add both 100,000 + 70 = 100,070.

Question 2.
Five hundred sixty thousand _____
560,000,

Explanation:
Standard form or expanded notation is a way of writing numbers to see the
math value of individual digits.
Numbers are separated into individual place values to write in numbers.
Five hundred sixty thousand = 560 x 1000 = 560,0 00.

Question 3.
Five million, eighty thousand, five _____
50,080,005,

Explanation:
Standard form or expanded notation is a way of writing numbers to see the
math value of individual digits.
Numbers are separated into individual place values to write in numbers.
Five million = 5 x 1,000,000,
Eighty thousand = 80 x 1000,
Five = 5,
Add all the numbers = 50,080,005.

Question 4.
Two million, four hundred thousand, seven hundred twenty ___
2,400,720,

Explanation:
Standard form or expanded notation is a way of writing numbers to see the
math value of individual digits.
Numbers are separated into individual place values to write in numbers.
Two million = 2 x 1,000,000,
Four hundred thousand = 400 x 1000,
Seven hundred twenty = 720,

Write each number in word form. (Lesson 1.1)

Question 5.
120, 450 _____
One hundred twenty thousand four hundred fifty,

Explanation:
Word form  and stand forms are both are reciprocal to each other.
Numbers are separated into individual place values to write in word form.

Question 6.
500, 312 _______
Five hundred thousand three hundred twelve,

Explanation:
Word form  and stand forms are both are reciprocal to each other.
Numbers are separated into individual place values to write in word form.

Question 7.
1,050,400 _____
One million fifty thousand four hundred,

Explanation:
Word form  and stand forms are both are reciprocal to each other.
Numbers are separated into individual place values to write in word form.

Question 8.
5,732,800 _____
Five million seven hundred thirty-two thousand eight hundred,

Explanation:
Word form  and stand forms are both are reciprocal to each other.
Numbers are separated into individual place values to write in word form.

Complete. (Lesson 1.2)

In 1,238,906:
One million two hundred thirty-eight thousand nine hundred six

Question 9.
the digit 8 stands for _____
8 stands for eight thousand,

Explanation:
Count the place values from right hand side at first,
So, 8 stands in thousand’s place.

Question 10.
the digit 9 stands for _____
9 stands for nine hundred,

Explanation:
Count the place values from right hand side at first,
So, 9 stands in hundred’s place.

Question 11.
the digit 1 stands for _____
1 stands for one million,

Explanation:
Count the place values from right hand side at first,
So, 1 stands in million’s place.

State the value of the digit 3 in each number. (Lesson 1.2)

Question 12.
538,426: ____
The value of the digit 3 is thirty thousand,

Explanation:
Count the place values from right hand side at first,
So, 3 stands in thousand’s place.

Question 13.
1,325,407: ____
The value of the digit 3 is three hundred thousands,

Explanation:
Count the place values from right hand side at first.
So, 3 stands in 300 thousand’s place.

Complete. (Lesson 1.2)

Question 14.
In 807,456, the digit ____ is in the thousands place.
7 is in the thousands place,

Explanation:
Count the place values from right hand side to the know the place value of 7,
So, 7 is in thousand’s place.

Question 15.
In 5,486,302, the digit ___ is in the millions place.
5 is in the millions place,

Explanation:
Count the place values from right hand side to know the place value of 5,
So, 5 is in millions place.

Question 16.
In 305,128, the digit 0 is in the ____ place.
0 is in the ten thousand place,

Explanation:
Count the place values from right hand side to know the place value of 0,
So, 0 is in ten thousand’s place.

Question 17.
In 7,614,892, the digit 6 is in the ____ place.
6 is in the hundred thousand’s place,

Explanation:
Count the place values from right hand side to know the place value of 6,
So, 6 is in hundred thousand’s place.

Question 18
918,230 = ___ + 10,000 + 8,000 + 200 + 30
9,00,000,

Explanation:
Count the place values from right hand side to know the place value of 9.
So, 9 is in millions’ place.
918,230 = 900,000 + 10,000 + 8,000 + 200 + 30.

Question 19.
538,417 = 500,000 + ____ + 8,000 + 400 + 10 + 7
30,000,

Explanation:
Count the place values from right hand side to know the place value of 9.
So, 3 is in ten thousand’s place.
538,417 = 500,000 + 30000 + 8,000 + 400 + 10 + 7.

Question 20.
6,000,000 + 30,000 + 90 = _____
9,030,090,

Explanation:
Standard form or expanded notation is a way of writing numbers to see the
math value of individual digits,
6,000,000 + 30,000 + 90 =9,030,090.

Fill each with >or <‘. (Lesson 1.3)

Question 21.
185,263 183,256
185,263 > 183,256,

Explanation:
First compare both the numbers,
by subtracting the smaller number 183,256 from bigger number 185,263,
then put the appropriate symbol in the circle.

Question 22.
5,060,345 995,863
5,060,345 > 995,863,

Explanation:
Count the place values of both the numbers.
in 5,060,345 place values are more.
So, put the greater than symbol in the circle.

Question 23.
899,506 900,650
899,506 < 900,650,

Explanation:
First compare both the numbers,
by subtracting the smaller number 899,506 from bigger number 900,650
then put the appropriate symbol in the circle.

Question 24.
231623 231,621
231,623 > 231,621,

Explanation:
First compare both the numbers,
by subtracting the smaller number 231,621 from bigger number 231,621
then put the appropriate symbol in the circle.

Order the number from greatest to least. (Lesson 1.3)

Question 5.

1,280,500    528,100    5280,100   528,010,

Explanation:
Arranging the numbers from greatest to smallest is known as descending order.

Find the rule. Then complete the number pattern. (Lesson 1.3)

Question 26.

Rule: ________
276,300   286,300    296,300    306,300    316,300,

Rule:
n + 1000,

Explanation:
Number patterns are the patterns in which a list of numbers follows a certain sequence.
Generally, the patterns establish the relationship between two numbers.
It is also known as the sequences of series in numbers.

Estimate by rounding. (Lesson 1.4)

Question 27.
7,512 + 3,281 _______
10,800,

Explanation:
Estimate of 7,512 is 7,500,
Estimate of 3,281 is 3,300,
7,500 + 3,300 = 10,800.

Question 28.
6,528 – 5,938 _______
500,

Explanation:
Estimate of 6,528 is 6500,
Estimate of 5,938 is 6000,
6,500 – 6,000  = 500.

Question 29.
1,592 × 5 _____
80,000,

Explanation:
Estimate of 1,592 is 1600,
1,600 x 5 = 8,000.

Question 30.
2,576 ÷ 3 _______
866,

Explanation:
Estimate of 2,576 is 2,600,
2,600 ÷ 3 =  866.

Estimate using front-end estimation with adjustment. (Lesson 1.4)

Question 31.
4,087 + 3,910 + 9,125
17,000,

Explanation:
Estimate of 4,087 is 4,000,
Estimate of 3,910 is 4,000,
Estimate of 9,125 is 9,000,
4,000 + 3,000 + 9,000 = 16,000,
000 + 900 + 100 = 1,000,
16,000 + 1,000 = 17,000.

Estimate using front-end estimation with adjustment. (Lesson 1.4)

Question 32.
8,685 + 6,319 + 7,752
22,700,

Explanation:
Estimate of 8,685 is 8,000,
Estimate of 6,319 is 6,000,
Estimate of 7,752 is 7,000,
8,000 + 6,000 + 7,000 = 21,000,
600 + 300 + 800 = 1,700,
21,000 + 1,700 = 22,700.

Question 33.
5,879 – 1,143
4,800,

Explanation:
Estimate of 5,879 is 5,000,
Estimate of 1,143 is 1,000,
5,000 – 1,000 = 4,000,
900 – 100 = 800,
4,000 + 800 = 4,800.

Question 34.
7,974 – 2,660
5,200,

Explanation:
Estimate of 7,974 is 7,000,
Estimate of 2,660 is 2,000,
7,000 – 2,000 = 5,000,
900 – 700 = 200,
5,000 + 200 = 5,200.

You may use your calculator where necessary. (Lesson 2.1)

Question 35.
Find the area of a square that has sides of length 96 inches.
________
9,216 square inches,

Explanation:
Area of a square = side x side,
Area = 96 x 96 square inches,
Area = 9,216 square inches.

Question 36.
Ms. Suarez has $5,651. Mr. Knox, has$853 more than Ms. Suarez. How much does Mr. Knox have?
___________
$6504, Explanation: Ms. Suarez has$5,651,
Mr. Knox has $5,651 +$853 = $6504, Mr. Knox have$6504.

You may use your calculator where necessary. (Lesson 2.1)

Question 37.
There are 176 gallons of gas in Tank A. There are 19 gallons less gas in Tank B.
How many gallons of gas are there in Tank B?
__157 gallons of gas______
157 gallons of gas,

Explanation:
Tank A    176 gallons of gas,
Tank B    176 – 19 = 157 gallons of gas.

Question 38.
A truck is loaded with 25 similar crates. The total weight of the crates is 2,000 pounds.
What is the weight of each crate?
___80 pounds______
80 pounds,

Explanation:
A truck is loaded with 25 similar crates,
The total weight of the crates is 2,000 pounds,
The weight of each crate 2,000 ÷ 25 = 80 pounds.

Multiply. (Lesson 2.2)

Question 39.
315 × 10 = __3,150_____
3,150,

Explanation:
315 x 10 = 300 x 10 + 10 x 10 + 5 x 10,
= 3000 + 100 + 50,
= 3,150.

Question 40.
25 × 100 = _2,500___
2,500,

Explanation:
100 x 25 = 20 x 100 + 5 x 100,
= 2000 + 500,
= 2,500.

Question 41.
238 × 1,000 = __238,000__
238,000,

Explanation:
238 x 1000 = 200 x 1000 + 30 x 1000 + 8 x 1000,
= 2,00,000 + 30,000 + 8,000,
= 238,000.

Question 42.
147 × 50 = _7,350___
7,350,

Explanation:
147 x 50 = 100 x 50 + 40 x 50 + 7 x 50,
= 5,000 + 2,000 + 350,
= 7,350.

Question 43.
63 × 200 = _12,600___
12,600,

Explanation:
60 x 200 + 3 x 200 = 12000 + 600,
= 12,600.

Question 44.
906 × 7,000 = __6,342,000__
6,342,000,

Explanation:
906 x 7,000 = 900 x 7,000 + 0 x 6,000 + 6 x 7,000,
=6,300,000 + 0 + 42,000
= 6,342,000.

Estimate by rounding. (Lesson 2.2)

Question 45.
41 × 58 ______
2,400,

Explanation:
41 x 58 = 40 x 60,
= 2,400.

Question 46.
297 × 32 _____
9,000,

Explanation:
300 x 30 = 9,000.

Question 47.
1,087 × 21= __22,000___
22,000,

Explanation:
1,100 x 20 = 22,000.

Question 48.
4.975 × 78 = __388.05___
388.05,
Estimate: 400,

Explanation:
4.975 X 78 =388.05,
Estimate of 4.975 is 5,
Estimate of 78 is 80,
So, 5 x 80 = 400.

Multiply. (Lesson 2.3)

Question 49.
19 × 102 = ____
1,900,

Explanation:
19 x 102,
102 = 10 x 10 = 100,
= 19 x 100,
= 1,900.

Question 50.
186 × 102 = __18,600__
18,600,

Explanation:
186 x 102 = 102 = 10 x 10 = 100,
= 186 x 100,
= 100 x 100 + 80 x 100 + 6 x 100,
= 10,000 + 8,000 + 600,
= 18,600.

Question 51.
65 × 103 = __65,000__
65,000,

Explanation:
65 x 103,
103 = 10 x 10 x 10 = 1,000,
= 65 x 1,000,
= 65,000.

Question 52.
154 × 103 = _1,54,000__
1,54,000,

Explanation:
154 x 103 = 103 = 10 x 10 x 10 = 1,000,
=154 x 1,000,
= 1,54,000.

Question 53.
82 × 45 = ____
3,600,

Explanation:
Estimate of 82 is 80, 80 x 45 = 80 x 40 + 80 x 5,
= 3,200 + 400,
= 3,600,

Check
82 x 45,
Multiply 82 by 5,
Multiply 82 by 4 tens,
410 + 3,280 = 3,690,

Question 54.
78 × 21 = __1,600___
1,600,

Explanation:
Given 78 X 21 we
Estimate of 78 is 80,80 x 20 = 1,600,
Check
78 x 21,
Multiply 78 by 20,
Multiply 78 by 1 ten,
1,560 + 78 = 1,638,

Question 55.
275 × 59 = __16,500__
16,500,

Explanation:
275 x 60 = 200 x 60 + 70 x 60 + 5 x 60,
= 12000 + 4200 + 300,
= 16,500
Check
275 x 59 = 16,225.

Question 56.
738 × 96 = _74,000___
74,000,

Explanation:
= 740 x 100 = 700 x 100 + 40 x 100 + 0 x 100,
= 70,000 + 4,000 + 0,
= 74,000,
Check
738 x 96 = 70,848,

Question 57.
4,672 × 73 = _327,040___
4,672 x 73,
4,672 x 70 = 327,040,
4,672 x 3 = 14,016,
327,040+14,016 = 341,056,
Check
4,700 x 70 = 3,29,000,

Question 58.
8,781 × 26 = _175,620___
8,672, x 20 = 175,620,
8,781 x 6 = 52,686,
175,620 + 52,686 = 2,28,306,
8,800 x 25 = 2,20,000.

Divide. (Lesson 2.5)

Question 59.
3,560 ÷ 10 = _356__
356,

Explanation:
3,560 ÷ 10,
3,560 is dividend and 10 is divisor
Count the number of zeros in dividend and divisor and
just move the decimal point one point to the left side.

Question 60.
1,900 ÷ 100 = _19___
19,

Explanation:
1,900 ÷ 100,
1,900 is dividend and 10 is divisor
Count the number of zeros in dividend and divisor and
just move the decimal point two points to the left side.

Question 61.
17,000 ÷ 1,000 = __17__
17,

Explanation:
17,000 ÷ 1,000,
17,000 is dividend and 1,000 is divisor
Count the number of zeros in dividend and divisor and
just move the decimal point 3 points to the left side.

Question 62.
900 ÷ 60 = __15__
15,

Explanation:
900 ÷ 60 = (900 ÷ 10) ÷ 6,
= 90 ÷ 6 =  15.

Question 63.
96,000 ÷ 400 = __240__
240,

Explanation:
96,00 ÷ 400 = (96,000 ÷ 100) ÷ 4,
= 9,60 ÷ 4,
=  240.

Question 64.
504,000 ÷ 9,000 = _56__
56,

Explanation:
504,000 ÷ 9,000 = (504,000 ÷ 1000) ÷ 9,
= 504 ÷ 9,
=  56.

Estimate. (Lesson 2.5)

Question 65.
4,593 ÷ 53 = __90__
90,

Explanation:
Estimate of 4,593 is 4,500,
Estimate of 53 is 50,
So, 4500 ÷ 50 = 90,
50 x 90 = 4,500.

Question 66.
6,298 ÷ 164 = __30__
30,

Explanation:
Estimate of 6,298 is 6,000,
Estimate of 164 is 200,
So, 6,000 ÷ 200 = 30,
200 x 30 = 6,000.

Question 67.
7,623 ÷ 4,451 = __2__
2,

Explanation:
Estimate of 7,623 is 8,000,
Estimate of 4,451 is 4,000,
So, 8,000 ÷ 4,000 = 2,
4,000 x 2 = 8,000.

Question 68.
4,239 ÷ 73 = _60___
60,

Explanation:
Estimate of 4,239 is 4,200,
Estimate of 73 is 70,
So, 4200 ÷ 70 = 60,
70 x 60 = 4,200,

Divide. (Lesson 2.6)

Question 69.
96 ÷ 16 = _6__
6,

Explanation:
96 ÷ 16,
16 rounds to 10.
6 × 10 = 60,
6 × 16 = 96,

Question 70.
57 ÷ 23 = __2 R 11__
2 R 11,

Explanation:
57 ÷ 23,
23 rounds to 20.
3 × 20 = 60,
3 × 23 = 69,
The estimated quotient is too big. Try 2.

Question 71.
459 ÷ 27 = _17___
17,

Explanation:
459 ÷ 27,
459 rounds to 500.
27 rounds to 30,
500 ÷ 30 = 16.6,

Question 72.
503 ÷ 15 = _33 R 8___
33 R 8,

Explanation:
503 ÷ 15,
503 rounds to 500.
15 rounds to 20,
20 x 25 = 500,
The quotient is about 33 and remainder is 8.

Simplify. (Lesson 2.7)

Question 73.
60 + 12 – 36 = _36__
36,

Explanation:
The order of operation in math is a set of rules revolving around 4 major operators.
According to the order of operations, there is a particular sequence which we need to follow,
on each operator while solving the given mathematical expression we apply DMAS rule.
DMAS is the elementary rule for the order of operation of the Binary operations.
This States that Division will be done before Multiplication,
Step 1: 60 + 12 = 72,
Step 2: 72 – 36 = 36.

Question 74.
10 × 9 ÷ 3 = __30__
30,

Explanation:
The order of operation in math is a set of rules revolving around 4 major operators.
According to the order of operations, there is a particular sequence which we need to follow,
on each operator while solving the given mathematical expression we apply DMAS rule.
DMAS is the elementary rule for the order of operation of the Binary operations.
This States that Division will be done before Multiplication,
Step 1: 9 ÷ 3 = 3,
Step 2: 10 x 3 = 30.

Question 75.
29 + 42 ÷ 6 = _36__
36,

Explanation:
The order of operation in math is a set of rules revolving around 4 major operators.
According to the order of operations, there is a particular sequence which we need to follow,
on each operator while solving the given mathematical expression we apply DMAS rule.
DMAS is the elementary rule for the order of operation of the Binary operations.
This States that Division will be done before Multiplication,
Step 1: 42 ÷ 6 = 7,
Step 2: 29 + 7 = 36.

Question 76.
(90 – 85) × 7 = _35__
35,

Explanation:
The order of operation in math is a set of rules revolving around 4 major operators.
According to the order of operations, there is a particular sequence which we need to follow,
on each operator while solving the given mathematical expression we apply DMAS rule.
DMAS is the elementary rule for the order of operation of the Binary operations.
This States that Division will be done before Multiplication,
Step 1 : 90 – 85 = 5,
Step 2: 5 x 7 = 35.

Question 77.
50 × 8 + 12 ÷ 4 = _403___
403,

Explanation:
The order of operation in math is a set of rules revolving around 4 major operators.
According to the order of operations, there is a particular sequence which we need to follow,
on each operator while solving the given mathematical expression we apply DMAS rule.
DMAS is the elementary rule for the order of operation of the Binary operations.
This States that Division will be done before Multiplication,
Step 1: 12 ÷ 4 = 3,
Step 2: 50 x 8 = 400,
Step 3: 400 + 3 = 403.

Question 78.
69 ÷ 3 – 3 + 10 = _30__
30,

Explanation:
The order of operation in math is a set of rules revolving around 4 major operators.
According to the order of operations, there is a particular sequence which we need to follow,
on each operator while solving the given mathematical expression we apply DMAS rule.
DMAS is the elementary rule for the order of operation of the Binary operations.
This States that Division will be done before Multiplication,
Step 1: 69 ÷ 3 = 23
Step 2: 23 – 3 = 20
Step 3: 20 + 10 = 30.

Evaluate. (Lesson 2.7)

Question 79.
56 + {12 – [18 – (3 + 9)]} = _62___
62,

Explanation:
According to the order of operations, there is a particular sequence which we need to follow,
on each operator while solving the given mathematical expression we apply BODMAS rule.
BODMAS is the elementary rule for the order of operation of the Binary operations.
The acronym stands for B – Brackets, O – Order of powers, D – Division,
M – Multiplication, A – Addition, and S – Subtraction.
Step 1: 3 + 9 = 12,
Step 2: 18 – 12 = 6,
Step 3: 12 – 6 = 6,
Step 4: 56 + 6 = 62.

Question 80.
100 ÷ (20 + 5) + [(18 – 3) × 4] = __64__
64,

Explanation:
According to the order of operations, there is a particular sequence which we need to follow,
on each operator while solving the given mathematical expression we apply BODMAS rule.
BODMAS is the elementary rule for the order of operation of the Binary operations.
The acronym stands for B – Brackets, O – Order of powers, D – Division,
M – Multiplication, A – Addition, and S – Subtraction.
Step 1: 20 + 5 = 25,
Step 2: 100 ÷ 25 = 4,
Step 3: 18 – 3 = 15,
Step 4: 15 x 4 = 60,
Step 5:  60 + 4 = 64.

Problem Solving

Question 81.
Tony had an equal number of cranberry bars and walnut bars. He gave away 66 cranberry bars.
He then had 4 times as many walnut bars as cranberry bars left. How many bars did he have at first?
176 bars at first,

Explanation:
Cranberry ‘c’ = ‘w’ Walnut bars,
4(c – 66) = w,
4c – 264=w,
4c – 264=c,
3c – 264=0(Zero),
3c = 264,
c = 88 cranberry bars,
w = 88 walnut bars,
88 + 88=176 bars at first,
check:
88 – 66 = 22 and 88 is 4 times 22.

Question 82.
Mrs. Turner had 20 yards of fabric at first. She made 5 similar curtains.
She used 3 yards of fabric for making each curtain. Then she used another 2 yards of fabric to
make a cushion cover. How much fabric does she have left?
3 yards,

Explanation:
Total fabric = 20 yards,
used to make curtains = 5 x 3 = 15,
used to make cushion cover = 2,
leftover = 20 – (15 + 2) = 20 – 17 = 3 yards.

Question 83.
At a school fair, a fifth-grade class sold 25 liters of orange juice.
The orange juice was sold in cups containing 200 milliliters and 300 milliliters.
An equal number of cups containing 200 milliliters and 300 milliliters were sold.
How many cups of orange juice did the class sell?
100 cups,

Explanation:
25L of orange juice = 25,000 ml,
200 + 300=500 ml,
25000 ml ÷  500 ml = 50 cups,
2 x 50 cups = 100 cups.

Question 84.
Mikhail used 220 inches of wire to make this figure.

The figure is made up of two identical triangles, a 15-inch by 12-inch rectangle and
a square of side 1 9 inches. What is the length of one side of each triangle if all the sides
of the triangles are equal in length?
15 inch is the length of one side of each triangle,

Explanation:
Rectangle = 15 + 12 + 15 +12 = 54 inches,
Square = 19 x 4 = 76 inches,
220 – ( 54 + 76) = 90 inches,
2 triangles = 6 sides = 90 ÷ 6 = 15 inch is the length of one side of each triangle.

Question 85.
A shop owner bought 260 handbags at 5 for $25. She then sold all of them at 2 for$1 8.
How much money did she make?
$1,040, Explanation: A shop owner bought 260 handbags at 5 for$25,
260 ÷ 5 = 52,
52 x 25 = 1300,
she bought the hand bag for $1300, She then sold all of them at 2 for$18.
260 ÷ 2 = 130,
130 x 18 = $2,340, She sold them for$2,340,
Total money she makes
$2,340 –$1,300 = $1,040. Solve. Show your work. Question 86. Alan scored a total of 14 points for answering all 15 questions on a math quiz. For every correctly answered question, Alan got 2 points. For every wrong answer, he lost 2 points. How many questions did he answer correctly? Answer: He answered 11 questions correctly, Explanation: For every correctly answered question, Alan got 2 points. For every wrong answer, he lost 2 points. Question 87. Beth and Lewis buy the same amount of fish flakes. If Beth feeds her goldfish 14 fish flakes each day, a container of flakes will last 20 days. If Lewis feeds his goldfish 8 fish flakes each day, how many more days will the container of flakes last for Lewis? Answer: The container will last 15 more days, Explanation: Beth feeds her goldfish 14 fish flakes each day, a container of flakes will last 20 days. 14 x 20 = 280, If Lewis feeds his goldfish 8 fish flakes each day. 280 ÷ 8 = 35, 35 days – 20 days = 15 days, The container will last 15 more days. Solve. Show your work. Question 88. Joan can pick 9 pounds of strawberries in one hour. a. How long does she take to pick 72 pounds of strawberries? Answer: 8 hours, Explanation: 72 pounds ÷ 9 pounds = 8, Joan takes 8 hours to pick 72 pounds. b. Joan is paid$12 per hour. How much does Joan earn if she picks twice the
total weight of strawberries in a.?
Joan earn $192, Explanation: 8 hrs x 2 = 16 hrs, 16 x$12 = $192, Joan earn$192.

Question 89.
There are 2,488 students in Washington School. There are 160 more students in Kent School.
The number of students in Bellow School is half the total number of students in
Washington School and Kent School. How many students are there in Bellow School?
There are 2,568 students in the Bellow school,

Explanation:
There are 2,488 students in Washington School.
There are 160 more students in Kent School.
2,488+ 160 = 2,648 students,
The number of students in Bellow School is half the total number of students in
Washington School and Kent School.
2,488 students + 2,648 students = 5,136 students,
Total students in Bellow School
5,136 students ÷ 2 = 2,568 students.

Question 90.
Jasmine mixes 1,250 milliliters of syrup with twice as much water to make lemonade.
She then pours the lemonade equally into 15 glasses.
Each glass has 250 ml of lemonade,

Explanation:
Jasmine mixes 1,250 milliliters of syrup with twice as much water to make lemonade,
1,250 x 2 = 2,500ml of water 1,250 + 2500= 3,750 ml,
She then pours the lemonade equally into 15 glasses.
3,750 ml ÷ 15 = 250 ml.

Must Try:

## Math in Focus Grade 3 Chapter 16 Practice 5 Answer Key Elapsed Time

This handy Math in Focus Grade 3 Workbook Answer Key Chapter 16 Practice 5 Elapsed Time provides detailed solutions for the textbook questions.

## Math in Focus Grade 3 Chapter 16 Practice 5 Answer Key Elapsed Time

Tell what time it will be.

Question 1.
2 hours after 8:00 P.M. _____________
Explanation:
By using a timeline we can calculate elapsed time:
2 hours after 8:00 PM means if we add 8 and 2 then we get 8+2=10 hours.

1. The start time and end times are labelled on an end of a timeline.
2. Between 8:00 and 10:00 are the hours of 9:00, which are marked on the timeline.
3. Between 8:00 and 10:00 there are 2 hours.

Question 2.
3 hours before 6:40 A.M. ______________
Explanation:
1. Calculating the elapsed time means finding the difference between two times.
2. To calculate the elapsed time, it is easiest to count up in hours.
3. Here asked 3 hours before the given time. So we need to subtract 6:40 And 3 hours then we get 6:40-3:00=3:40.
4. The elapsed time is 3 hours 40 minutes A.M.

Question 3.
30 minutes after 1:36 P.M. _______________
Explanation:

1. The start time and end times are labelled on an end of a timeline.
2. Between 1:36 and 2:01 are the hours of 2:00, which are marked on the timeline.
3. We subtract the 36 minutes of 1:36 from the 60 minutes to get 24 minutes. There are 24 minutes from 1:36 pm and 2:00 pm.
4. Between 1:36 pm and 1:40 there are 4 minutes.
5. Between 1:40 pm and 2:00 pm there are 25 minutes.
6. We need to calculate for 30 minutes. And from 2:00 pm to 2:01 pm, there is 1 minute.
7. Now adding all the minutes, 4 +25+1=30.
8. Finally, 1:36 pm after 30 minutes are 2:01 pm.

Question 4.
45 minutes before 7:05 A.M. _____________
Here given end time that is 7:05 AM. We need to calculate the start time.

Explanation:
1. Now I calculated the start time by using the given 45 minutes.
2. First I wrote 7:05 AM on the timeline as an end date. From there I started counting start times.
3. Then I take the earliest time to 7:05 AM that is 7:00 AM. Between both timings, there are 5 minutes.
4. And then I take 6:30 AM which is nearer to 7:00 AM. Between both timings, there are 30 minutes.
5. And we need to calculate for extra 10 minutes. From 6:30 to 6:20 there are 10 minutes so I took 6:20 AM.
6. Now add all the minutes 5+30+10=45 minutes.
7. The start time is 6:20 AM.

Question 5.
3 hours after 1 0:25 A.M. ______________
Explanation:

Explanation:
1. Now I calculated the end time.
2. I wrote the start time on the timeline that is 10:25 AM.
3. I subtracted the 25 minutes of 10:25 AM from the 60 minutes to get 35 minutes. There are 35 minutes from 10:25 am and 11:05 am.
4. Between 11:05 am and 12:05 pm there is 1 hour.
5. Between 12:05 to 1:05 PM there is 1 hour.
6. Between 1:05 Pm to 1:30 Pm there is 25 minutes.
7. add all the hours1 hour+1 hour=2 hours.
8. Now add minutes 35 min+25 min=60 min which is equal to 1 hour.
9. Finally, 3 hours. The 10:25 after 3 hours is 1:30 PM.

Question 6.
2 hours before 1:20 P.M. ______________
Explanation:

1. Already given end time that is 1:20 PM. We need to calculate the start time means before 2 hours.
2. We subtracted 20 min of 1:20 PM from the 60 minutes to get 40 min. So we calculated the difference of 40 min we get the time of 12:35 PM.
3. We calculated for 20 min because from their 1 hour will be completed. So we had taken 12:15. From 12:15 to 12:35 there is 1 hour.
4. And from 12:15 Pm to 11:15 AM there is 1 hour.
5. Finally we calculated for 2 hours. The start time is 11:15 AM.

Example

Question 7.
7:45 P.M. to 8:15 P.M. _____________
Explanation:

1. The start time and end times are labelled at the end of the timeline.
2. Between 7:45 PM and 8:15 PM are the hours of half an hour which is marked on the timeline.
3. We subtract the 45 min of 7:45 PM from the 60 min to get 15 min. There are 15 minutes from 7:45 PM to 8:00 PM.
4. From 8:00 PM to 8:15 PM there are 15 minutes.
5. We add the minutes together. 15+15=30 minutes.
6. The elapsed time is 30 minutes.

Question 8.
2:30 P.M. to 4:50 P.M. _______________
Explanation:

1. The start time and end times are labelled at the end of the timeline.
2. Between 2:30 PM and 4:50 PM are the hours of 3:00 and 4:00 PM which are marked on the timeline.
3. We subtract 30 min of 2:30 from the 60 min to get 30 min. There are 30 minutes from 2:30 and 3:00 PM.
4. Between 3:00 and 4:00 there is 1 hour.
5. Between 4:00 and 4:50 there are 50 minutes.
6. Adding minutes together. 30+50=80. Such that, we already know, 1 hour=60 minute. So, we can say 80 minutes is nothing but 1 hour 20 minutes.       (80-60=20)
7. Now by adding hours 1+1=2 hours.
8. Hence the resultant is 2 hour 20 minutes.

Question 9.
7:45 A.M. to 9:50 A.M _______________
Explanation:

1. The start time and end times are labelled at the end of the timeline.
2. Between 7:45 AM and 9:50 AM are the hours of 8:00 and 9:00 AM which are marked on the timeline.
3. We subtract 45 min of 7:45 from the 60 min to get 15 min. There are 15 minutes from 7:45 and 8:00 AM.
4. Between 8:00 and 9:00 there is 1 hour.
5. Between 9:00 and 9:50 there are 50 minutes.
6. Adding minutes together. 15+50=65. Such that, we already know, 1 hour=60 minute. So, we can say 80 minutes is nothing but 1 hour 5 minutes.       (65-60=5)
7. Now by adding hours 1+1=2 hours.
8. Hence the resultant is 2 hours 5 minutes.

Question 10.
11:30 P.M. to 2:10 A.M. _______________

Explanation:
1. The start time and end times are labelled at the end of the timeline.
2. Between 11:30 PM and 2:10 AM are the hours of 12:00, 1:00, 2:00 AM which are marked on the timeline.
3. We subtract 30 min of 11:30 from the 60 min to get 30 min. There are 30 minutes from 11:30 and 12:00 AM.
4. Between 12:00 and 1:00 there is 1 hour.
5. Between 1:00 and 2:00 there is 1 hour.
6. Between 2:00 and 2:10 there are 10 minutes.
8. Now by adding hours 1+1=2 hours.
9. Hence the resultant is 2 hours 40 minutes.

Question 11.
11:25 A.M. to 3:10 P.M. _______________
Explanation:

1. The start time and end times are labelled at the end of the timeline.
2. Between 11:25 AM and 12:00 PM are the hours of 12:00, 1:00, 2:00, 3:00 PM which are marked on the timeline.
3. We subtract 25 min of 11:25 from the 60 min to get 35 min. There are 35 minutes from 11:25 and 12:00 PM.
4. Between 12:00 and 1:00 there is 1 hour.
5. Between 1:00 and 2:00 there is 1 hour.
6. Between 2:00 and 3:00 there is 1 hour.
7. Between 3:00 and 3:10 there are 10 minutes
8. Now by adding hours 1+1+1=3 hours.
9. Hence the resultant is 3 hours 45 minutes.

Write the correct time. Draw the missing hands on each clock.

Question 12.

1. Start time is given and need to calculate the end time.
2. 3 hours 15 minutes after the time is 12:45.
3. From 9:30 PM to 10:30 Pm there is 1 hour.
4. Between 10:30 PM to 11:30 Pm there is 1 hour.
5. Between 11:30 to 12:30 PM there is 1 hour.
6. Between 12:30 to 12:45 there is 15 minutes.
7. Adding hours we get 1+1+1=3 hours.
8. The minutes are 15 minutes.
9. Hence resultant is 3 hours 15 minutes that is 12:45.

Question 13.

Explanation:
1. We already know the end time that is 2:00 AM
2. We need to calculate the elapsed time, 2 hours and 45 minutes.
3. Between 2:00 to 1:00 there is 1 hour.
4. Between 1:00 to 12:00 there is 1 hour.
5. 12:00 to 11:15 there are 45 minutes.
6. So I had taken 11:45 PM for 12:00 AM to 45 minutes.

Question 14.
Suki exercises every morning. She starts at 6:30 A.M. and ends at 8:15 A.M. How long does she exercise?

Starting time=6:30 AM
Ending time=8:15 AM

1. The start time and end times are labelled at the end of the timeline.
2. Between 6:30 AM and 8:15 AM are the hours of 7:00, 8:00 AM which are marked on the timeline.
3. We subtract 30 min of 6:30 from the 60 min to get 30 min. There are 30 minutes from 6:30 and 7:00 AM.
4. Between 7:00 and 8:00 there is 1 hour.
5. Between 8:00 and 8:15 there is 15 minutes.
9. Hence the resultant is 1 hour 45 minutes.
Explanation:

Question 15.
Devon started reading a book at 2:35 P.M. She took 3 hours 10 minutes to finish the book. What time did she finish reading the book?

Starting time=2:35 PM
Ending time=X
The given time=3 h 10 min.

Explanation:
1. The start time is labelled on the timeline that is 2:35 PM
2. Subtract 35 minutes of 2:35 from 60 minutes to get 25 min. There is 25 min from 2:35 and 3:00 PM.
3. From there we need to calculate 3 h 10 min after time.
4. Start from 3:00 PM, between 3:oo PM to 4:00 PM there is 1 hour.
5. Between 4:00 PM to 5:00 PM there is 1 hour.
6. Between 5:00 PM to 5:35 PM there are 35 minutes.
7. Between 5:35 to 5:45 there are 10 minutes.
8. Likewise we need to calculate the ending time.
9. Adding all the minutes:25+35+10=70 minutes. We can write 70 as 1 hour 10 minutes. (1 hour=60 minutes).
10. Finally, the result of 3 h 10 min is 5:45 PM.

Question 16.
Lissa went to the library. She was there for 2 hours 15 minutes. She left the library at 5:40 P.M. What time did she get to the library?
We need to calculate starting time.
We can say it as another way 2 hours 15 minutes before 5:40 PM.

Explanation:
1. The end time is labelled on the timeline that is 5:40 PM
2. Subtract 40 min of 5:40 from 60 min to get 20. The 20 min before 5:40 is 5:20 PM.
3. Now calculate for 1 hour that is 5:20 to 4:20.
4. Now we need to calculate for 55 minutes. The 55 minutes before 4:20 is 3:25 PM.

Question 17.
Marcus visited his friend’s house from 11:50 A.M. to 3:15 P.M. How long was his visit?

Starting time=11:50 AM
Ending time=3:15 PM

1. The start time and end times are labelled at the end of the timeline.
2. Between 11:50 AM and 12:00 PM are the hours of 12:00, 1:00, 2:00, 3:00 PM which are marked on the timeline.
3. We subtract 50 min of 11:50 from the 10 min to get 10 min. There are 10 minutes from 11:50 and 12:00 PM.
4. Between 12:00 and 1:00 there is 1 hour.
5. Between 1:00 and 2:00 there is 1 hour.
6. Between 2:00 and 3:00 there is 1 hour.
7. Between 3:00 and 3:15 there are 15 minutes
8. Now by adding hours 1+1+1=3 hours.
9. Hence the resultant is 3 hours 25 minutes.

Question 18.
Mr. Nelson took 3 hours 30 minutes to decorate his classroom. He started at 9:20 A.M. What time did he finish?

Starting time=9:20 AM
The elapsed time is given: 3 h 30 min.
Ending time=X

Explanation:
1. I labelled starting time on the timeline that is 9:20 AM
2. Subtract 20 min of 9:20 from the 60 min to get 60-20=40.
4. And from there, calculate according to the elapsed time.
5. Now calculate for 3 hours and then calculate for 30 minutes.
6. Now observe the above timeline in which we represented all the calculations.
7. Finally, the end time is 12:45 PM.

Question 19.
Mrs Martin’s flight landed at 2:25 A.M. The flight was 4 hours 45 minutes long. What time did the flight take off?

Starting time=2:25 AM
Elapsed time=4 h 45 min
Ending time=X

Explanation:
1. I labelled starting time on the timeline that is 2:25 AM
2. Subtract 25 min of 2:25 from the 60 min to get 60-25=35.
4. And from there, calculate according to the elapsed time.
5. Now calculate for 4 hours and then calculate for 1o minutes because we calculated already 35 minutes.
6. Now observe the above timeline in which we represented all the calculations.
7. Finally, the end time is 7:10 AM.

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## Math in Focus Grade 3 Chapter 16 Practice 4 Answer Key Subtraction of Time

This handy Math in Focus Grade 3 Workbook Answer Key Chapter 16 Practice 4 Subtraction of Time provides detailed solutions for the textbook questions.

## Math in Focus Grade 3 Chapter 16 Practice 4 Answer Key Subtraction of Time

Subtract

Example

Question 1.

So, 8 h 20 min – 7 h 15 min
= _______ h _________ min.

______ h – ______ h = ______ h
______ min – ______ min = ______ min
______ h – ______ min = ______ h ______ min
We measure time in hours, minutes, and seconds. There are 60 minutes in an hour and 60 seconds in a minute.
1. Subtract the hours
2. Subtract the minutes
3. If the minutes are negative, add 60 to the minutes and subtract 1 from hours.
Explanation:
Step 1: Subtract the hours.
=8hours-7hours
=1 hour
Step 2: Subtract the minutes.
=20min-15min
=5 min
Hence, the resultant from Step 1 and Step 2 together is the answer (1hour 5minutes).

Question 2.

So, 4 h 35 min – 1 h 15 min
= _______ h _________ min.

______ h – ______ h = ______ h
______ min – ______ min = ______ min
______ h – ______ min = ______ h ______ min
We measure time in hours, minutes, and seconds. There are 60 minutes in an hour and 60 seconds in a minute.
1. Subtract the hours
2. Subtract the minutes
3. If the minutes are negative, add 60 to the minutes and subtract 1 from hours.
Explanation:
Step 1: Subtract the hours.
=4hours-1hours
=3 hour
Step 2: Subtract the minutes.
=35min-15min
=20 min
Hence, the resultant from Step 1 and Step 2 together is the answer (3hour 20minutes).

Question 3.

So, 3 h 55 min – 2 h 30 min
= _______ h _________ min.

______ h – ______ h = ______ h
______ min – ______ min = ______ min
______ h – ______ min = ______ h ______ min
We measure time in hours, minutes, and seconds. There are 60 minutes in an hour and 60 seconds in a minute.
1. Subtract the hours
2. Subtract the minutes
3. If the minutes are negative, add 60 to the minutes and subtract 1 from hours.
Explanation:
Step 1: Subtract the hours.
=3hours-2hours
=1 hour
Step 2: Subtract the minutes.
=55min-30min
=25 min
Hence, the resultant from Step 1 and Step 2 together is the answer (1hour 25minutes).

Subtract

Question 4.

Explanation:
We measure time in hours, minutes, and seconds. There are 60 minutes in an hour and 60 seconds in a minute.
1. Subtract the hours
2. Subtract the minutes
3. If the minutes are negative, add 60 to the minutes and subtract 1 from hours.
Here in the question, 2 h 20 min and 1 h 50 min.
Explanation:
Step 1: Subtract the hours.
=2hours-1hours
=1 hour
Step 2: Subtract the minutes.
=20min-50min
=-30 min
The minutes are negative. So follow step 3.
Step 3: add 60 to the minutes and subtract 1 from hours.
=60+20
=80
Subtract 1 from 2
=2-1
=1
Now calculate 1 h 80 min and 1 h 50 min
If we subtract hours 1-1=0
If we subtract min 80-50=30
Hence, the resultant from Step 1 and Step 2 together is the answer (0hour 30minutes).

Question 5.

Explanation:
1. Subtract the hours
2. Subtract the minutes
3. If the minutes are negative, add 60 to the minutes and subtract 1 from hours.
Here in the question, 2 h 20 min and 1 h 50 min.
Explanation:
Step 1: Subtract the hours.
=5hours-2hours
=3 hour
Step 2: Subtract the minutes.
=15min-25min
=-10 min
The minutes are negative. So follow step 3.
Step 3: add 60 to the minutes and subtract 1 from hours.
=60+15
=75
Subtract 1 from 2
=5-1
=4
Now calculate 4 h 75 min and 2 h 25 min
If we subtract hours 4-2=2
If we subtract min 75-25=50
Hence, the resultant from Step 1 and Step 2 together is the answer (2hour 50minutes).

Question 6.

Explanation:
1. Subtract the hours
2. Subtract the minutes
3. If the minutes are negative, add 60 to the minutes and subtract 1 from hours.
Here in the question, 6 h 10 min and 1 h 55 min.
Explanation:
Step 1: Subtract the hours.
=6hours-1hours
=5 hour
Step 2: Subtract the minutes.
=10min-55min
=-45 min
The minutes are negative. So follow step 3.
Step 3: add 60 to the minutes and subtract 1 from hours.
=10+60
=70
Subtract 1 from 6
=6-1
=5
Now calculate 5 h 70 min and 1 h 55 min
step 4: If we subtract hours 5-1=4
step 5: If we subtract min 70-55=15
Hence, the resultant from Step 4 and Step 5 together is the answer (4hour 15minutes).

Question 7.

Explanation:
1. Subtract the hours
2. Subtract the minutes
3. If the minutes are negative, add 60 to the minutes and subtract 1 from hours.
Here in the question, 9 h 40 min and 4 h 45 min.
Explanation:
Step 1: Subtract the hours.
=9hours-4hours
=5 hour
Step 2: Subtract the minutes.
=40min-45min
=-5 min
The minutes are negative. So follow step 3.
Step 3: add 60 to the minutes and subtract 1 from hours.
=40+60
=100
Subtract 1 from 9
=9-1
=8
Now calculate 8 h 100 min and 4 h 45 min
step 4: If we subtract hours 8-4=4
step 5: If we subtract min 100-45=55
Hence, the resultant from Step 4 and Step 5 together is the answer (4hour 55minutes).

Solve.

Question 8.
Rita takes 3 hours 5 minutes to sew a dress. Tara takes 2 hours 40 minutes to sew a similar dress. How much longer does Rita take to sew the dress than Tara?
Answer: 25 minutes longer Tita take to sew the dress than Tara.
The time Rita takes to sew a dress=3 h 5 minutes.
The time Tara takes to sew a dress=2 h 40 minutes.
1. Subtract the hours
2. Subtract the minutes
3. If the minutes are negative, add 60 to the minutes and subtract 1 from hours.
Here in the question, 3 h 5 min and 2 h 40 min.
Explanation:
Step 1: Subtract the hours.
=3hours-1hours
=1 hour
Step 2: Subtract the minutes.
=5min-40min
=-35 min
The minutes are negative. So follow step 3.
Step 3: add 60 to the minutes and subtract 1 from hours.
=60+5
=65
Subtract 1 from 3
=3-1
=2
Now calculate 2 h 65 min and 2 h 40 min
step 4: If we subtract hours 2-2=0
step 5: If we subtract min 65-40=25
Hence, the resultant from Step 4 and Step 5 together is the answer (0hour 25minutes).

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## Math in Focus Grade 4 Cumulative Review Chapters 5 and 6 Answer Key

Practice the problems of Math in Focus Grade 4 Workbook Answer Key Cumulative Review Chapters 5 and 6 to score better marks in the exam.

## Math in Focus Grade 4 Cumulative Review Chapters 5 and 6 Answer Key

Concepts and Skills
Complete. Use the data in the table. (Lesson 5.1)

The ages of four cousins are shown.
8, 12, 10, 6

Question 1.
The sum of their ages is ___ years.
Sum of their ages = 36 years.

Explanation:
The ages of four cousins are shown.
8, 12, 10, 6
Sum of their ages = 8 + 12 + 10 + 6
= 20 + 10 + 6
= 30 + 6
= 36 years.

Question 2.
The mean age of the cousins is ___ years.
Mean age of their ages = 9 years.

Explanation:
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are.
Sum of their ages = 36 years.
Number of people = 4.
Mean age of their ages = Sum of their ages ÷ Number of people
= 36 ÷ 4
= 9 years.

Answer each question. Use the data in the line plot. (Lesson 5.2)
A group of hikers made a line plot to show the number of mountains they climbed. Each ✗ represents one hiker.

Question 3.
What is the median number of mountains climbed? ____
Median number of mountains climbed = 4.

Explanation:
Number of mountain hikers = 1 1 1 2 3 3 3 3 4 4 5 5 5 6 6 6 6 6
Median number of mountains climbed = (4 + 4) ÷ 2
= 8 ÷ 2
= 4.

Question 4.
What is the range of the set of data? ____
The range of the set of data = 1 to 6.

Explanation:
The range of a set of data is the difference between the highest and lowest values in the set.
Number of mountain hikers = 1 1 1 2 3 3 3 3 4 4 5 5 5 6 6 6 6

Question 5.
What is the mode of the set of data? ____
The mode of the set of data = 6.

Explanation:
The mode is the value that appears most often in a set of data values.
1 mountain climbed by 3 people.
2 mountain climbed by 1 person.
3 mountain climbed by 4 people.
4 mountain climbed by 2 people.
5 mountain climbed by 3 people.
6 mountain climbed by 5 people.

Make a stem-and-leaf plot to show the data. (Lesson 5.3)
Question 6.
A group of friends went bowling and recorded these scores.
75 73 79 84 98 64 84 67

Explanation:
Arrange the scores given: 64 67 73 75 79 84 84 98.
To make a stem and leaf plot, each observed value must first be separated into its two parts:

1. The stem is the first digit or digits;
2. The leaf is the final digit of a value;
3. Each stem can consist of any number of digits; but.
4. Each leaf can have only a single digit.

Complete. Use the data in your stem-and-leaf plot.
Question 7.
____ is the mode.
84 is the mode.

Explanation:
Scores given: 64 67 73 75 79 84 84 98.
64 – 1
67 – 1
73 – 1
75 – 1
79 – 1
84 – 2
98 – 1.

Question 8.
___ is the median.
77 is the median.

Explanation:
Scores given: 64 67 73 75 79 84 84 98.
Median = (75 + 79) ÷ 2
= 154 ÷ 2
= 77.

Question 9.
___ is the range.
64 to 98 is the range.

Explanation:
Scores given: 64 67 73 75 79 84 84 98.

Question 10.
___ is an outlier.
84 to 98 is an outlier.

Explanation:
84 – 79 = 5.
73 – 67 = 6.
98 – 84 = 14.

Question 11.
How do the mode and median each change if you disregard the outlier?
The effect of removing one outlier data point from the set. No matter what value we add to the set, the mean, median, and mode will shift by that amount but the range and the IQR will remain the same.

Explanation:
Outlier is an extreme value in a set of data which is much higher or lower than the other numbers. Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data.

Write more likely, less likely, equally likely, certain, or impossible. (Lesson 5.4)
A bag has 8 blue marbles and 2 orange marbles. Describe the likelihood of each outcome.
Question 12.
An orange marble is chosen. _____
Probability of orange marbles is chosen = 1 ÷ 5 or $$\frac{1}{5}$$ .

Explanation:
Number of blue marbles = 8.
Number of orange marbles = 2.
Total marbles in bag = 8 + 2 = 10.
Probability of orange marbles is chosen = Number of orange marbles ÷ Total marbles in bag
= 2 ÷ 10
= 1 ÷ 5 or $$\frac{1}{5}$$ .

Question 13.
A blue marble is chosen. ____
Probability of blue marbles is chosen = 4 ÷ 5 or $$\frac{4}{5}$$ .

Explanation:
Number of blue marbles = 8.
Number of orange marbles = 2.
Total marbles in bag = 8 + 2 = 10.
Probability of blue marbles is chosen = Number of blue marbles ÷ Total marbles in bag
= 8 ÷ 10
= 4 ÷ 5 or $$\frac{4}{5}$$ .

Question 14.
A red marble is chosen. ____
Probability of red marbles is chosen = 0.

Explanation:
Number of blue marbles = 8.
Number of orange marbles = 2.
Number of red marbles = 0.
Total marbles in bag = 8 + 2 = 10.
Probability of red marbles is chosen = Number of red marbles ÷ Total marbles in bag
= 0 ÷ 10
= 0.

Question 15.
A blue or an orange marble is chosen. ____
Probability of orange or blue marbles is chosen = 1.

Explanation:
Number of blue marbles = 8.
Number of orange marbles = 2.
Total marbles in bag = 8 + 2 = 10.
Probability of blue marbles is chosen = Number of blue marbles ÷ Total marbles in bag
= 8 ÷ 10
= 4 ÷ 5 or $$\frac{4}{5}$$ .
Probability of orange marbles is chosen = Number of orange marbles ÷ Total marbles in bag
= 2 ÷ 10
= 1 ÷ 5 or $$\frac{1}{5}$$ .
Probability of orange or blue marbles is chosen = (Number of orange marbles + Number of blue marbles) ÷ Total marbles in bag)
= (8 + 2) ÷ 10
= 10÷ 10
= 1.

Solve. Use the scenario above. (Lesson 5.4)
Question 16.
How would you change the number of each colored marble in the bag so that it is more likely that an orange marble is chosen?

Explanation:
Number of blue marbles = 8.
Number of orange marbles = 2.
Total marbles in bag = 8 + 2 = 10.

Look at the spinner. Write the probability of each outcome as a fraction. (Lesson 5.5)

Question 17.
Probability of landing on 2 = ____
Probability of landing on 2 = 2 ÷ 3 or $$\frac{2}{3}$$

Explanation:
Number of 2 on spinner = 4.
Total numbers on spinner = 6.
Probability of landing on 2 = Number of 2 on spinner ÷ Total numbers on spinner
= 4 ÷ 6
= 2 ÷ 3 or $$\frac{2}{3}$$

Question 18.
Probability of landing on 6 = ____
Probability of landing on 6 = 0.

Explanation:
Number of 6 on spinner = 0.
Total numbers on spinner = 6.
Probability of landing on 6 = Number of 6 on spinner ÷ Total numbers on spinner
= 0 ÷ 6
= 0.

Add or subtract. Write each answer in simplest form. (Lessons 6.1 and 6.2)
Question 19.
$$\frac{3}{4}$$ + $$\frac{1}{12}$$ + $$\frac{1}{6}$$ =
$$\frac{3}{4}$$ + $$\frac{1}{12}$$ + $$\frac{1}{6}$$ = $$\frac{11}{12}$$

Explanation:
$$\frac{3}{4}$$ + $$\frac{1}{12}$$ + $$\frac{1}{6}$$ =
= [(9 + 1) ÷ 12] + $$\frac{1}{12}$$
= $$\frac{10}{12}$$ + $$\frac{1}{12}$$
= (10 + 1) ÷ 12
= $$\frac{11}{12}$$

Question 20.
$$\frac{9}{10}$$ – $$\frac{1}{5}$$ – $$\frac{1}{2}$$ =
$$\frac{9}{10}$$ – $$\frac{1}{5}$$ – $$\frac{1}{2}$$ = $$\frac{1}{5}$$

Explanation:
$$\frac{9}{10}$$ – $$\frac{1}{5}$$ – $$\frac{1}{2}$$ =
= [(9 – 2) ÷ 10] – $$\frac{1}{2}$$
= $$\frac{7}{10}$$ – $$\frac{1}{2}$$
= (7 – 5) ÷ 10
= 2 ÷ 10
= $$\frac{1}{5}$$

Write the amount of water in each set of 1-liter containers as a mixed number. (Lesson 6.3)
Question 21.

Amount of 2 jars = 1 $$\frac{1}{5}$$L.

Explanation:
Amount of water in first jar = 1L.
Amount of water in second jar = $$\frac{1}{5}$$L.
Amount of 2 jars = Amount of water in first jar + Amount of water in second jar
= 1 + $$\frac{1}{5}$$
= (5 + 1) ÷ 5
= $$\frac{6}{5}$$
= 1 $$\frac{1}{5}$$L.

Question 22.

Amount of three jars = 2$$\frac{1}{2}$$L.

Explanation:
Amount of water in first jar = 1L.
Amount of water in second jar = 1L.
Amount of water in third jar = $$\frac{1}{2}$$L.
Amount of three jars = Amount of water in first jar + Amount of water in second jar + Amount of water in third jar
= 1 + 1 + $$\frac{1}{2}$$
= 2 + $$\frac{1}{2}$$
= (4 + 1) ÷ 2
= $$\frac{5}{2}$$
= 2$$\frac{1}{2}$$L.

Express the shaded part of each figure as a mixed number or an improper fraction. (Lessons 6.4 and 6.5)
Question 23.

Explanation:
Mixed number of the shaded figure = 2$$\frac{3{4}$$
Improper fraction of the shaded figure = (8 + 3) ÷ 4
= 11 ÷ 4 or $$\frac{11}{4}$$

Question 24.

Explanation:
Improper fraction of the shaded figure = $$\frac{12}{8}$$
Mixed number of the shaded figure = $$\frac{12}{8}$$
= 1$$\frac{4}{8}$$

Express each improper fraction as a mixed number. (Lesson 6.5)
Question 25.
$$\frac{9}{7}$$ = ____
$$\frac{9}{7}$$ = 1$$\frac{2}{7}$$

Explanation:
$$\frac{9}{7}$$ = 1$$\frac{2}{7}$$

Question 26.
$$\frac{20}{9}$$ = ____
$$\frac{20}{9}$$ = 2$$\frac{2}{9}$$

Explanation:
$$\frac{20}{9}$$ = 2$$\frac{2}{9}$$

Express each mixed number as an improper fraction. (Lesson 6.5)
Question 27.
3$$\frac{2}{5}$$ = ____
3$$\frac{2}{5}$$ = $$\frac{17}{5}$$

Explanation:
3$$\frac{2}{5}$$ = (15 + 2 ) ÷ 5 = $$\frac{17}{5}$$

Question 28.
2$$\frac{8}{9}$$ = ____
2$$\frac{8}{9}$$ = $$\frac{26}{9}$$

Explanation:
2$$\frac{8}{9}$$ = (18 + 8) ÷ 9 = $$\frac{26}{9}$$

Question 29.
2 + $$\frac{2}{5}$$ + $$\frac{1}{10}$$ = ____
2 + $$\frac{2}{5}$$ + $$\frac{1}{10}$$ = $$\frac{25}{10}$$

Explanation:
2 + $$\frac{2}{5}$$ + $$\frac{1}{10}$$ = ](10 + 2) 5] + $$\frac{1}{10}$$
= $$\frac{12}{5}$$ + $$\frac{1}{10}$$
= (24 + 1) ÷ 10
= $$\frac{25}{10}$$

Question 30.
3 – $$\frac{3}{4}$$ – $$\frac{5}{8}$$ = ___
3 – $$\frac{3}{4}$$ – $$\frac{5}{8}$$ = $$\frac{23}{8}$$

Explanation:
3 – $$\frac{3}{4}$$ – $$\frac{5}{8}$$ = 3 – [(6 – 5)÷ 8]
= 3 – $$\frac{1}{8}$$
= (24 – 1) ÷ 8
= $$\frac{23}{8}$$

check (✓) each set in which $$\frac{2}{5}$$ of the figures are shaded. (Lesson 6.7)
Question 31

Explanation:
(✓) each set in which $$\frac{2}{5}$$ of the figures are shaded.
Fraction of square figure = Number of shaded squares ÷ Total number of squares
= 8 ÷ 16
= 1 ÷ 2 or $$\frac{1}{2}$$
Fraction of circle figure = Number of shaded circles ÷ Total number of circles
= 6 ÷ 15
= 2 ÷ 5 or $$\frac{2}{5}$$
Fraction of triangle figure = Number of shaded triangles ÷ Total number of triangles
= 4 ÷ 20
= 1 ÷ 5 or $$\frac{1}{5}$$

Solve. (Lesson 6.7)
Question 32.
$$\frac{2}{3}$$ of 15 = ___
$$\frac{2}{3}$$ of 15 = 10.

Explanation:
$$\frac{2}{3}$$ of 15 = 2 ×5 = 10.

Question 33.
$$\frac{3}{5}$$ of 40 = ___
$$\frac{3}{5}$$ of 40 = 24.

Explanation:
$$\frac{3}{5}$$ of 40 = 3 × 8 = 24.

Problem Solving
Question 34.
Teams A, B, C, and D were in a tournament. The average score of the 4 teams was 92. Team A scored 78 points,
Team B scored 95 points, and Team C scored 88 points.

a. How many points did Team D score?
Points Team D scored = 107.

Explanation:
Points Team A scored = 78.
Points Team B scored = 95.
Points Team C scored = 88.
Points Team D  scored = ??.
The average score of the 4 teams was 92.
=> (Points Team A scored + Points Team B scored + Points Team C scored  + Points Team D scored) ÷ 4 = 92.
=> (78 + 95 + 88 + ??) ÷ 4 = 92.
=> (173 + 88 + ??) ÷ 4 = 92.
=> (261 + ??) ÷ 4 = 92 × 4
=> 261 + ?? = 92 × 4
=> 261 + ?? = 368.
=> ?? = 368 – 261
=> ?? = 107.
Points Team D scored = 107.

b. Find the range of the scores. Hence, state the difference in score between the winning team and the losing team.
Range of the scores = 78 to 107.
29 is the difference in score between the winning team and the losing team.

Explanation:
Scores scored by teams = 78 88 95 107.
Points Team A scored = 78.
Points Team B scored = 95.
Points Team C scored = 88.
Points Team D  scored = 107.
Difference:
Highest score scored – Least score scored
= 107 – 78
= 29.
Losing team are Team A,B,C. Winning team is A.

Question 35.
Michael scored 15, 21, and 24 in the first three basketball games of the season.
a. What is his mean score?
His mean score = 20.

Explanation:
Score scored by Michael in the first three basketball games of the season = 15, 21, 24.
The mean is the arithmetic average of a set of given numbers. The median is the middle score in a set of given numbers. The mode is the most frequently occurring score in a set of given numbers.
His mean score = score scored ÷ Number of games
= (15 + 21 + 24) ÷ 3
= (36 + 24) ÷ 3
= 60 ÷ 3
= 20.

b. What is the range of his scores?
Range of his scores = 15 to 24.

Explanation:
Score scored by Michael in the first three basketball games of the season = 15, 21, 24.
Range of his scores = 15 to 24.

c. How many points must he score in the next game to achieve a mean score of 27?
48 more points must he score in the next game to achieve a mean score of 27.

Explanation:
His mean score = score scored ÷ Number of games
=> 27 = (15 + 21 + 24 + ?? ) ÷ 4
=> 27 = (36 + 24 + ?? ) ÷ 4
=> 27 = (60 + ?? ) ÷ 4
=> 27 × 4 = 60 + ??
=> 108 – 60 = ??
=> 48 = ??.

Question 36.
Samuel and Kenneth collect sports cards. The average number of cards they have is 248. Samuel has 3 times as many cards as Kenneth. How many cards does each boy have?
Number of sports cards Kenneth collected = 124.
Number of sports cards Samuel collected = 372.

Explanation:
Samuel has 3 times as many cards as Kenneth.
Let Number of sports cards Kenneth collected be X.
=> Number of sports cards Samuel collected = 3 × Number of sports cards Kenneth collected
= 3  × X = 3X.
The average number of cards they have is 248.
=> (Number of sports cards Samuel collected + Number of sports cards Kenneth collected) ÷ 2 = 248.
=> (3X + X) ÷ 2 = 248
=> 4X ÷ 2 = 248.
=> 4X = 248 × 2
=> 4X = 496.
=> X = 496 ÷ 4
=> X = 124.
Number of sports cards Samuel collected = 3X = 3 × 124 = 372.

Question 37.
A group of students made a list of the states where they were born. The line plot shows the number of times the letter A’ appears in the name of each state. Each ✗ represents one state.

Complete. Use the data in the line plot.
a. What is the mode of the set of data? ____
Mode of the set of data = 1.

Explanation:
Number of times A appears in states = 0 1 1 1 2 2 3 4 4
The mode is the most frequently occurring score in a set of given numbers.
Mode of the set of data = 1.

b. What is the mean number of times the letter A’ appears? ___
Mean number of times the letter A’ appears = 2.

Explanation:
The mean is the arithmetic average of a set of given numbers.
Number of times A appears in states = 0 1 1 1 2 2 3 4 4
mean number of times the letter A’ appears = (0 + 1 + 1 + 1 + 2 + 2 + 3 + 4 + 4) ÷ 9
= 18 ÷ 9
= 2.

c. Is the name of a state more likely to have 1 or 2 As? Explain your answer.
Yes, the state going to have more likely 2As because mean number of times the letter A’ appears = 2.

Explanation:
Yes state is going to have 2 As because average letters in the states name going to be 2 that menas in their names 2As are likely to be.

d. According to the data, what is less likely to happen? Explain your answer.
According to the data, its less likely to happen that minimum As likely to be 1 and maximum 2 As in every name of state not more.

Explanation:
Well, its less likely to happen that minimum As likely to be 1 and maximum 2 As in every name of state not more.

Question 38.
The stem-and-leaf plot shows the number of pages in 8 books.

a. Which stem has only odd numbers for its leaves?
Stem 3 is having only odd numbers for its leaves.

Explanation:
All the numbers ending with 1,3,5,7 and 9 are odd numbers. For example, numbers such as 11, 23, 35, 47 etc.
Stem 2 – 1 5
Stem 3 – 0 5 5 7.
Stem 4 – 3 6.

b. Find the median of the set of data.
Median of set = 35.

Explanation:

Number of pages = 21, 25, 30, 35, 35, 37, 43, 46.
Median of set = (35 + 35) ÷ 2
= 70 ÷ 2
= 35.

c. Find the mode of the set of data. ___
Mode of the set of data = 35.

Explanation:
The mode is the value that appears most often in a set of data values.
Number of pages = 21, 25, 30, 35, 35, 37, 43, 46.

21 – 1 time.
25 – 1 time.
30 – 1 time.
35 – 2 time.
37 – 1 time.
43 – 1 time.
46 – 1 time.

d. Find the range of the set of data. ____
Range of the set of data – 21 to 46.

Explanation:
Number of pages = 21, 25, 30, 35, 35, 37, 43, 46.

e. Which of the above measures tells you the difference in the number of pages between the thickest and the thinnest books? ___
Range of the set of data above measures tells you the difference in the number of pages between the thickest and the thinnest books.

Explanation:
Range of the set of data above measures tells you the difference in the number of pages between the thickest and the thinnest books.

f. Is there an outlier in the set of data? Explain your answer. ___
No, there is no outlier in the set of data because there is no much difference in the data measurements.

Explanation:
There is no outlier in the set of data because there is no much difference in the data measurements.

Question 39.
A cube is numbered from 1 to 6 and tossed once. What is the probability of tossing
a. a 5 or a 6? ___
Probability of tossing 5 = 1 ÷ 6 or $$\frac{1}{6}$$
Probability of tossing 6 = 1 ÷ 6 or $$\frac{1}{6}$$

Explanation:
A cube is numbered from 1 to 6 and tossed once.
Total numbers on cube = 6.
Probability of tossing 5 = Number of 5 side ÷ Total numbers on cube
= 1 ÷ 6 or $$\frac{1}{6}$$
Probability of tossing 6 = Number of 6 side ÷ Total numbers on cube
= 1 ÷ 6 or $$\frac{1}{6}$$

b. an odd number? ___
Probability of odd number = 1 ÷ 2 or $$\frac{1}{2}$$

Explanation:
odd number on cube = 1, 3 , 5.
Total numbers on cube = 6.
Probability of odd number = odd number on cube ÷ Total numbers on cube
= 3 ÷ 6
= 1 ÷ 2 or $$\frac{1}{2}$$

Question 40.
Sasha has 40 stamps in her collection. 12 of them are from foreign countries.

a. What fraction of the stamps are foreign stamps?
Fraction of the stamps are foreign stamps = 3 ÷ 10 or  $$\frac{3}{10}$$

Explanation:
Number of stamps in her collection Sasha has = 40.
Number of stamps of them are from foreign countries = 12.
Fraction of the stamps are foreign stamps = Number of stamps of them are from foreign countries ÷ Number of stamps in her collection Sasha has
= 12 ÷ 40
= 3 ÷ 10 or  $$\frac{3}{10}$$

b. What fraction of the stamps are U.S. stamps?
3 ÷ 10 or  $$\frac{3}{10}$$  are fraction of the stamps are U.S. stamps.

Explanation:
Fraction of the stamps are U.S. stamps = Number of stamps of them are from U.S.  countries ÷ Number of stamps in her collection Sasha has
= 12 ÷ 40
= 3 ÷ 10 or  $$\frac{3}{10}$$

Question 41.
A string is 1 foot long. Blake cuts What fraction of the string is left?

Explanation:
Length of the string = 1 foot.

Question 42.
Pedro scored $$\frac{1}{4}$$ of all the goals scored during a soccer game. He scored 2 goals. How many goals were not scored by Pedro?
Number of goals were not scored by Pedro = 6.

Explanation:
Points scored by Pedro $$\frac{1}{4}$$ of all the goals scored during a soccer game.
Let all goals be X.
Points soccer game scored = X × $$\frac{1}{4}$$ = 2.
=> X = 2 × 4
=> X = 8.
Points Pedro scored = 2.
Number of goals were not scored by Pedro = Points soccer game scored – Points Pedro scored
= 8 – 2
= 6.

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